Pseudo-homogeneous reaction rates

In order to exemplify the potential of micro-channel reactors for thermal control, consider the oxidation of citraconic anhydride, which, for a specific catalyst material, has a pseudo-homogeneous reaction rate of 1.62 s at a temperature of 300 °C, corresponding to a reaction time-scale of 0.61 s. In a micro channel of 300 pm diameter filled with a mixture composed of N2/02/anhydride (79.9 20 0.1), the characteristic time-scale for heat exchange is 1.4 lO" s. In spite of an adiabatic temperature rise of 60 K related to such a reaction, the temperature increases by less than 0.5 K in the micro channel. Examples such as this show that micro reactors allow one to define temperature conditions very precisely due to fast removal and, in the case of endothermic reactions, addition of heat. On the one hand, this results in an increase in process safety, as discussed above. On the other hand, it allows a better definition of reaction conditions than with macroscopic equipment, thus allowing for a higher selectivity in chemical processes. 

The pseudo-homogeneous reaction rate for the packed reactor is... 

If there is no change of density during the reaction, the concentration can be suitably measured in moles per unit volume and the linear velocity will be denoted by if reactor is packed, the velocity v is taken to be the volume flow rate divided by the total cross-sectional area of the reactor. (The mean velocity through the interstices of the packed bed is v/e, where is the void fraction.) Also, let c/z) be the concentration of at a distance z from the inlet and r(ej, T) be the pseudo-homogeneous reaction rate in moles per unit reactor volume per unit time. If is the cross-sectional area of the reactor then in a unit of time... 

Thus, when proceeding with energy efficiency calculations, PTEF definitions using pseudo homogenous reaction rates r or r" + are preferred. For this reason data analysis is developed on the basis of equation (9-4). 

Since we are interested in pseudo-homogeneous reaction rates ... 

While photocatalytic reactions are frequently considered to be pseudo-homogeneous reactions with a rate based on either the unit volume of irradiated catalyst or the total reactor volume (Chapter I), definitions of the PTEF can be given as follows ... 

The amount of A that leaves the volume element during the time increment At consists of three similar terms. The amount of A that accumulates within the volume element during time At is (ACa)2tiR(AR)(Az), and the amount of A that is generated by chemical reaction within the volume element is vArv2nR(AR)(Az)(At), where rv is the reaction rate expressed in pseudo homogeneous form [i.e., the number of moles transformed per unit time per unit of total reactor volume (voids plus solid)]. 

The units on the rate constants reported by DeMaria et al. indicate that they are based on pseudo homogeneous rate expressions (i.e., the product of a catalyst bulk density and a reaction rate per unit mass of catalyst). It may be assumed that these relations pertain to the intrinsic reaction kinetics in the absence of any heat or mass transfer limitations. 

Here the pseudo-homogeneous rate r is related to the surface reaction rate r" through the area of active catalyst per unit volume of reactor. Assuming further a plug-flow regime, the integration of the mass balance equation for this simple rate expression gives an expression for CO conversion ... 

So, rm, rvs, rs, and rt are the appropriate rates for expressing the intrinsic catalytic reaction rate, whereas ru and R are phenomenological rates, used for reactor design. More specifically, ru is also called the pseudo-homogeneous rate (Schmidt, 2005). 

The rate-based models usually use the two-film theory and comprise the material and energy balances of a differential element of the two-phase volume in the packing (148). The classical two-film model shown in Figure 13 is extended here to consider the catalyst phase (Figure 33). A pseudo-homogeneous approach is chosen for the catalyzed reaction (see also Section 2.1), and the corresponding overall reaction kinetics is determined by fixed-bed experiments (34). This macroscopic kinetics includes the influence of the liquid distribution and mass transfer resistances at the liquid-solid interface as well as dififusional transport phenomena inside the porous catalyst. 

For the system considered here, the reaction is slow as compared to the mass transfer rate. For this reason the pseudo-homogeneous approach is used, the reaction being accounted for in the liquid bulk only. 

In certain cases, the assumption of a pseudo-homogeneous catalytic mechanism might be valid [19], and the reaction rate equation would depend only on the concentrations in the liquid phase. 

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