Reaction-diffusion regime mass transfer time

Here tm is the mass-transfer time. Only under slow reaction kinetic control regime can intrinsic kinetics be derived directly from lab data. Otherwise the intrinsic kinetics have to be extracted from the observed rate by using the mass-transfer and diffusion-reaction equations, in a manner similar to those defined for catalytic gas-solid reactions. For instance, in the slow reaction regime,... 

To determine the kinetic parameters, we use the differential reactor. In this continuous flow system, the variation in concentration between the inlet and outlet of the reactor should be small and finite. The conversions should be around 5-10%. Under these conditions, the diffusive and mass transfer effects are avoided, assuring a kinetic regime for the determination of the kinetic parameters. Unlike the case of the batch system, the spatial time and consequently, the inlet flow and the mass or volume of the reactor are varied. Therefore, the reaction rate is directly determined. 

Here tD and fr are the diffusion and reaction times, respectively, and k, is the mass-transfer coefficient in the absence of reaction. For the fast reaction regime, diffusion and reaction occur in parallel in the liquid film, while for the slow reaction regime, there is no reaction in the liquid film and the mass transfer can be considered to occur independently of reaction in a consecutive manner. For the slow reaction regime, the following subregimes can be defined ... 

At the lower temperature (783 K open symbols in Fig. 70) a substantially different behavior is observed. The imide band (A in Fig. 69 bottom) decreases quasi-linearly with the elapsed time (see Eq. 24). The aromatic band (V in Fig. 70 top) is complex, revealing two distinct decomposition patterns. At the beginning (first half) of the normalized time a slow linear decrease is observed, followed by a fast decrease. The decrease of the imide band and the change of the aromatic band in the second part of the curve are typical for a film diffusion-controlled reaction of shrinking particles in a gas flow in the Stokes regime. To confirm this observation a new mathematical model is used to fit the curves [321]. Starting from Eq. 20, the reaction velocity ks is substituted with kg=D Rf1 [321]. D is the diffusion velocity and kg the mass transfer coefficient between fluid and particle. The differential equation is solved and the time necessary to reduce a particle from a starting radius R0 to Rt is obtained [see Eq. (22)] [321],... 

These expressions can be physically explained for both examples. In the case of a parallel coupling, the global operation time is dominated by the smallest fundamental time, i.e. the fastest phenomena. For the parallel reactions, the conversion of reactant A evolves as fast as the fastest reaction. In this case, the fastest phenomenon dominates. In contrast, for serial phenomena, the slowest phenomenon dominates the conversion rate of reactant D submitted to mass transfer and heterogeneous reaction proceeds at the rate of the slowest phenomenon, leading to a possible diffusion regime or chemical regime. 

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