Rates intrinsic reaction rate

When the effectiveness factors for both reactions approach unity, the selectivity for two independent simultaneous reactions is the ratio of the two intrinsic reaction-rate constants. However, at low values of both effectiveness factors, the selectivity of a porous catalyst may be greater than or less than that for a plane-catalyst surface. For a porous spherical catalyst at large values of the Thiele modulus s, the effectiveness factor becomes inversely proportional to (j>S9 as indicated by equation 12.3.68. In this situation, equation 12.3.133 becomes... 

The types of systems we deal with are primarily gas-solid (Section 9.1) and gas-liquid (Section 9.2). In these cases, we assume first- or second-order kinetics for the intrinsic reaction rate. This enables analytical expressions to be developed in some situations for the overall rate with transport processes taken into account. Such reaction models are incorporated in reactor models in Chapters 22 and 24. 

Following Carbeny (1976), in this book the term rate coefficient is used for the proportionality coefficients kt in the typical rate expression of the form r] = kJ(C). To simplify the following analysis, a first-order elementary reaction is considered. Then the intrinsic reaction rate can be... 

On the other hand, if kg —> °° or kg ks, the resistance to die overall rate is owing to the intrinsic reaction rate and CG — C s. The rate-controlling step is the reaction rate and the overall rate is... 

For example, consider a second order reaction. In this case, the intrinsic reaction rate is... 

Reaction-limited second-order reaction For a second-order reaction of the form 2A —> products, or in the more general case of a reaction of the form a A + bB -> products of second order with respect to A, the intrinsic reaction rate is... 

If kf —> oo or kf km, then by the rate-controlling step concept, the resistance to the overall rate is due to the intrinsic reaction rate and thus... 

Reactor model for a first-order reaction To illustrate the effect of pressure drop, consider an isothermal two-phase fixed-bed operation (gas-solid system). In terms of a reactant, the intrinsic reaction rate is... 

Here, the simple case of a first-order reaction is presented. The intrinsic reaction rate in each phase is... 

The reaction is carried out over a silver gauze or low surface supported catalyst at 600—700°C, indicating a very fast chemical reaction. This implies that determination of the intrinsic reaction rate in laboratory reactors is complicated by the interference of heat and mass transfer limitations. To avoid this problem, studies have been made at much lower temperatures, which in turn run the risk of being non-representative. 

The second factor to consider is the catalyst conditions and the catalyst-particles, environment. From the point of view of the effectiveness factor, the size, shape, porosity, metal-loading, and other internal characteristics, must be the same. Otherwise, the intrinsic reaction rate and selectivity will be compromised. In practice there will be a trend to reduce costs by using less metal. This will change the process markedly, and other adjustments will be required. 

With the use of microprocess technology, the fluorination with DAST can be performed under decomposition conditions in continuous-flow mode [50], Temperatures of 90-100 °C and reaction times of 60-120 min are necessary for high conversions in order to compensate for the slow intrinsic reaction rate. A continuous quality control allows regulation of the process parameters (PAT, process analytical technology). A throughput of 5-10kg/day using three parallel modules was achieved. 

As discussed in Sec. 7, the intrinsic reaction rate and the reaction rate per unit volume of reactor are obtained based on laboratory experiments. The kinetics are incorporated into the corresponding reactor model to estimate the required volume to achieve the desired conversion for the required throughput. The acceptable pressure drop across the reactor often can determine the reactor aspect ratio. The pressure drop may be estimated by using the Ergun equation... 

Intrinsic reaction rate constant, s overall apparent rate constant, s solubility coefficient, cur liquid-atm/mol stirrer speed, RPM partial pressure, atm... 

Table I. Summary of Intrinsic Reaction Rates in Various Solvents... 

Substituting the second Damkohlcr number Da, which is defined as the ratio of the intrinsic reaction rate to the maximum rate of reactant supply. 

Koros and Nowak [45] designed a more complex test based on the fact that the intrinsic reaction rate is proportional to the concentration of active sites in the... 

The intrinsic reaction rate has been measured in a discontinuous slurry stirred tank reactor and in a continuous microtrickle bed reactor (6 ). This last one is represented in Figure 1 Both methods lead to rather similar expressions for the intrin-sid rate equation r(mol/kg Pd. s)... 

Observed transport limitations in the studies given in Table I depend upon the magnitude of the intrinsic reaction rate. Petroleum hydrodesulfurization (19-21), certain types of petroleum hydrogenations (22), or chemical decomposition reactions (11) are liquid-limiting and proceed slowly enough that only internal particle diffusion or combined pore diffusion and liquid-to-solid resistances are controlling. Chemical... 

C = oxygen concentration at the reaction surface, kg = convective mass transfer coefficient, ks = intrinsic reaction rate constant,... 

A, cross sectional area, m2 k. intrinsic reaction rate constant, 1/s... 

Fig. 15. Changes in effective diffusivity of methanol in SAPO-34 and intrinsic reaction rate constants for methanol conversion on SAPO-34 as a function of the coke content in crystals with average sizes of 0.25 and 2.5 m (89).

For the particle sizes used in industrial reactors (> 1.5 mm), intraparticle transport of the reactants and ammonia to and from the active inner catalyst surface may be slower than the intrinsic reaction rate and therefore cannot be neglected. The overall reaction can in this way be considerably limited by ammonia diffusion through the pores within the catalysts [211]. The ratio of the actual reaction rate to the intrinsic reaction rate (absence of mass transport restriction) has been termed as pore effectiveness factor E. This is often used as a correction factor for the rate equation constants in the engineering design of ammonia converters. 

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