Mass transfer limitations experimental values

External mass transfer limitations, which cause a decrease in both the reaction rate and selectivity, have to be avoided. As in the batch reactor, there is a simple experimental test in order to verify the absence of these transport limitations in isothermal operations. The mass transfer coefficient increases with the fluid velocity in the catalyst bed. Therefore, when the flow rate and amount of catalyst are simultaneously changed while keeping their ratio constant (which is proportional to the contact time), identical conversion values should be found for flow rate high enough to avoid external mass transfer limitations.[15]... 

Transport Limitation For the estimation of the mass transport limitation, Equation (20) has an important drawback. In many cases neither the rate constant k nor the reaction order n is known. However, the Weisz-Prater criterion, cf. Equation (21), which is derived from the Thiele modulus [4, 8], can be calculated with experimentally easily accessible values, taking < < 1 for any reaction without mass transfer limitations. However, it is not necessary to know all variable exactly, even for the Weisz-Prater criterion n can be unknown. Reasonable assumptions can be made, for example, n - 1, 2, 3, or 4 and / is the particle diameter instead of the characteristic length. For the gas phase, De can be calculated with statistical thermodynamics or estimated common values are within the range of 10-5 to 10 7 m2/s. In the liquid phase, the estimation becomes more complicated. A common value of qc for solid catalysts is 1,300 kg/m3, but if the catalyst is diluted with an inert material, this... 

P12C-2 Use the references given in Ind. Eng. Chem. Prod. Res. Lev. /4, 226 (1975) to define the iodine value, saponification number, acid number, and experimental setup. Use the slurry reactor analysis to evaluate the effects of mass transfer and determine if there are any mass transfer limitations. 

The interest of using reciprocal values is that the experimental plot of as a function of must be a straight line parallel to e line corresponding to Levich s result for the mass-transfer-limited case, which passes through the origin. The ordinate value of the intercept of this straight line at = q is 4 -f-... 

In Figure 2 the experimental data of benzaldehyde steady state production rate are reported as a function of the gas flow rate. An increase in the reaction rate occurred above a flow rate of 1.7 cm s, and remained constant at higher values. This indicates that external mass transfer limitations occur for flow rates less than 1.7 cm s. Because of this aU the runs carried out for investigating the influence of toluene concentration were performed at a flow rate of 2.5 cm s-i. 

The calculated values of for subjects E and F were smaller than for subjects A through D but larger than observed from samrated water by a factor of about two. If a mass transfer limitation in the soil were the cause for this increased then from Equation 11.5 we would estimate that a = 1. If so, then we would expect = Q /2, which is a httie larger than was experimentally observed assuming that = in the satnrated water experiments. Based on experiments from saturated water,... 

Effect of gas-liquid mass transfer Different opinions on the importance of mass transfer limitations have been uttered by Satterfield and Huff (81,82,94) and Zaldl et al. (54) and Deckwer et al. (87). Satterfield and Huff (81) assxuned a bubble diameter of eUaout 2 mm and concluded that the FTS in slurry phase may be significantly limited by gas-liquid mass transfer. New experimental results do, however, confirm that in the molten paraffin system bubble diameters are less than 1 mm (53-55). With this low value and the high gas holdup observed in FT liquid f ase, i.e., eq. (8), high interfacial areas are obtained. Therefore slgniflccuit mass transfer can be excluded and for the catalyst systems studied until now the FT process in slurry phase is mainly reaction controlled (54,87). In addition, it follows from the reactor model used by Satterfield and Huff (81) that the relative mass transfer resistance is given by (95)... 

It is, however, possible to select fairly accurate A values because it varies within a rather narrow range experimental results reported vary between 0.1 and 0.4 Btu/h-ft-°F, excluding vacuum conditions [9]. Other order of magnitude values that have been reported as 4 x 10 J/s-cm-K [16] or 3 x 10 cal/s-cm-K [19] are also based on the latter results. Bearing in mind the lesser impact of internal heat transport compared with internal mass transfer limitations, relatively little attention has been paid to correlations of A inside pellets. 

The measured iso-amylenes conversion values in three runs of the pilot plant, under identical experimental conditions (Table 2) were 70.97 %, 81.26 % and 78.77 %. The simulated value, found for the same working conditions, is 76 %. As observed, taking into consideration the accuracy of the measurements, a fairly good agreement appears between the simulated and experimental conversion values. However, further improvements are needed concerning the kinetic data, the flow model of the reaction zone and the mass transfer limitations around the catalyst pellet. 

The inlet conditions for the numerical simulations are based on the experimental conditions. The simulations are performed with the three different models for internal diffusion as given in Section 2.3 to analyze the effect of internal mass transfer limitations on the system. The thickness (100 pm), mean pore diameter, tortuosity (t = 3), and porosity ( = 60%) of the washcoat are the parameters that are used in the effectiveness factor approach and the reaction-diffusion equations. The values for these parameters are derived from the characterization of the catalyst. The mean pore diameter, which is assumed to be 10 nm, hes in the mesapore range given in the ht-erature (Hayes et al., 2000 Zapf et al., 2003). CO is chosen as the rate-limiting species for the rj-approach simulations, rj-approach simulations are also performed with considering O2 as the rate-hmiting species. 

The operation of a PFR in a differential mode, i.e., at low values of A fA such that dfA A fA, provides some real benefits in regard to acquiring experimental data. Use of a differential reactor of any type helps to eliminate any heat and mass transfer limitations, although tests should still be conducted to verify their absence but, perhaps more importantly, it simplifies the rate expression, rm, as this function is now approximately constant throughout the reactor whether a change in the volume of the system occurs or not, thus, if fA in = 0 and fA out = fA, equation 4.20 is simply... 

Rh/Ce02 catalyst. Radial diffusion could be neglected in the model because of the high values of the Bodenstein number (>200) due to fast radial diffusion. Therefore, DR[ d c/dx ) + (l/r)(dc/dr)] = 0 in Equation 12.7. The model also involved the assumption that mass transfer limitations are obvious neither in the channel (diffusion to the catalyst layer) nor in the catalyst layer (pore diffusion). Moreover, an excellent isothermal behavior of the microchannel was confirmed by a good fit of the calculated values with the experimental results at a wide range of ethanol and water partial pressures, steam to carbon ratios, and temperatures. 

It was assumed that mass transfer limitations are not present due to the absence of catalysts and that the reactor behaves as a plug-flow reactor. A sequential method for determining the parameter values was employed, which is reported elsewhere (Ancheyta and Sotelo, 2000). The minimization of the objective function, based on the sum of square errors between the experimental and calculated product compositions, was applied to And the best set of kinetic parameters. This objective function was solved using the least-squares criterion with a nonlinear regression procedure based on Marquardt s algorithm. 

In an experimental wetted wall column, pure carbon dioxide, is absorbed in water. The mass transfer rate is calculated using the penetration theory, application of which is limited by the fact that the concentration should not teach more than 1 per cent of the saturation value at a depth below the surface at which the velocity is 95 per cent of the surface velocity. What is the maximum length of column to which the theory can be applied if the flowrate of water is 3 cm3/s per cm of perimeter ... 

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

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