Intraparticle mass-transfer resistance

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. 

Adsorption According to Fernandez and Carta (1996), who studied mass transfer in agitated reactors, the relative importance of external and intraparticle mass transfer resistances is strongly dependent on the solution composition. They used the following dimensionless number ... 

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. 

The effectiveness factor is very low, indicating that intraparticle mass transfer resistance is very significant. The gas-liquid mass transfer resistance is also important, as expected. On the other hand, the liquid-solid mass transfer resistance is negligible. As a result, the rate of reaction in the slurry reactor is about 50 times higher than that in the trickle-bed. Therefore, in cases of such high rates of reaction, the slurry reactor is a better choice, although the gas-liquid mass transfer and the filtration of the catalyst may be a problem. 

The analysis of the trickle-bed runs indicate that intraparticle mass transfer resistance is very significant. Gas-liquid mass transfer may also have a significant resistance. This is an important consideration in the decision process of using a slurry or a trickle-bed reactor. 

If enzymes are immobilized by copolymerization or microencapsulation, the intraparticle mass-transfer resistance can affect the rate of enzyme reaction. In order to derive an equation that shows how the mass-transfer resistance affects the effectiveness of an immobilized enzyme, let s make a series of assumptions as follows ... 

The analysis of intraparticle mass-transfer resistance requires the knowledge of the effective diffusivity Ds of a substrate in an immobilized matrix, such as agarose, agar, or gelatin. Gels are porous... 

During transport, both external and intraparticle mass transfer resistances play a role to a varying degree. A first step in adsorber design is to predict or... 

We now look at the mathematical equations for a general isothermal steady-state model for the trickle-bed reactor, which takes into account external mass-transfer resistances, i.e., gas-liquid and liquid-solid, axial dispersion, and the intraparticle mass-transfer resistances, along with the intrinsic kinetics occurring at the catalyst surface. Since many practical reactions can be characterized as... 

Historically, the throughput problem has been addressed by heuristics for scale-up of conventional packed beds for multicomponent separations. The most recent scale-up analyses, focusing on intraparticle mass-transfer resistance as a limiting factor, have led away from the traditional long columns to several alternative geometries (108, 109, 110). 

The effect of temperature was studied from 25 C to 75 C (Fig.6). The conversion was found to increase marginally with temperature. At temperatures of 50 C and 75°C there was practically no change in conversion, bringing into picture the intraparticle mass transfer resistance. 

Of course most industrial catalytic reactors (except fluidized bed catalytic reactors) use relatively large particle sizes for the catalyst to avoid the excessive pressure drop associated with fine particles. This gives rise to intraparticle mass transfer resistances. However, in most industrial reactors, but not all, the gas flowrate is quite large rendering external mass transfer resistances usually negligible. 

Kinetic factors will lead to dispersion of the fronts being much more important for favorable isotherms. Intraparticle mass-transfer resistance can be eliminated or decreased by using peUicular packings, reducing particle size or increasing particle permeability as shown in Fig. 3.4-4. 

Reactions requiring both a gaseous and a liquid reactant are usually performed in trickle-bed reactors in which the gas and liquid are pumped counter- or co-currently through a bed of catalyst particles [53, 54). Many of these systems encounter mass-transfer limitations as a result of intraparticle mass-transfer resistance, liquid-film resistance, liquid maldistribution and channelling. To overcome these problems, membrane reactors have been used for chemical reactions as well as biological conversions. 

Calculated conversions of butynediol (B) and hydrogen (A) with different sizes of catalyst particles are given in Fig. 8 with Dp as a parameter. The calculations are performed with a fixed value of the volumetric mass transfer coefficient, kLa, but including the liquid-solid and the intraparticle mass transfer resistances. 

It can be noticed that the conversions steadily decrease with increasing particle diameter, hence increasing mass transfer resistances, except for a reactor diameter of 10 cm, where they pass a minimum. This phenomenon can be explained by the fact that the catalyst accumulation in the reactor can compensate the decrease of the reaction rate caused by liquid-solid and intraparticle mass transfer resistances. If the intraparticle diffusional resistances are excluded, the overall behavior does not chcinge but the effect is less pronounced. 

The three-phase Robinson-Mahoney reactor (a continuous gas and liquid flow) consisted of a fixed catalyst basket and a magnetic stirrer. The reactor system was automated to ensure reliable and reproducible experiments. Liquid samples of the product stream were taken by an automatic on-line valve and analysed by a gas chromatograph with fused silica capillary column and FI detector. Detailed information on the apparatus [11] and the hydrogenation procedure can be found elsewhere [10]. Gas-liquid and liquid-solid mass transfer resistance were avoided by adjusting the agitation and catalyst loading. An intraparticle mass transfer resistance could not be avoided and this was added to the reactor model in parameter estimation [11]. 

The kinetic parameters of the rate expressions were defined under an intraparticle mass transfer resistance, which was significant for all compounds except the solvent. The mass transfer resistance was most pronounced at the beginning of the experiment and became weaker as the catalyst activity decreased. The rate of naphthalene hydrogenation rate was clearly faster than the rate of tetralin, which was also seen as more severe intraparticle mass transfer resistance of naphthalene than of tetralin, hydrogen or decalins. 

The example demonstrates that the intraparticle mass transfer resistance plays a crucial role and it cannot be discarded, since this would lead to a large error in the reactor sizing. 

A trickle bed reactor model was developed for the Esterification reactions studied. This model incorporates the contribution of intraparticle mass transfer resistances. The kinetic equations already developed were used for the respective esterification reactions. Experimental data were obtained in a 25 mm diameter glass trickle bed reactor at different concentrations of reactants, flow rates and temperatures. The performance of the reactor was measured in terms of the conversions of the acids obtained at the exit of the reactor. The model predictions were compared with experimental data at different operating conditions. This model would be useful in predicting the performance of a trickle bed reactor for esterification reactions in general. 

Effectiveness factors are used to estimate the intraparticle mass-transfer resistances in commercial reactor. 

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