Formulation of Reaction Rate Expressions

For process modeling proposes the effective chemical reaction rate has to be expressed as a function of the liquid bulk composition x, the local temperature T, and the catalyst properties such as its number of active sites per catalyst volume c, its porosity e, and its tortuosity t. As discussed in Section 5.4.2, the chemical reaction in the catalyst particles can be influenced by internal and external mass transport processes. To separate the influence of these transport resistances from the intrinsic reaction kinetics, a catalyst effectiveness factor p is introduced by 

The catalyst effectiveness factor depends on the parameters defined in Section 5.4.2 

In correspondence ivith the guidelines given above, the catalyst effectiveness is mostly only a weak function of p, and y. Therefore p = //( ). The latter function is available in analytical form for first-order reactions [38]. In the general case, it has to be determined from the numerical solution of the catalyst particle balances, as done for instance in [35, 39-42]. In the case of negative reaction orders, multiple effectiveness factors can be obtained [32]. This is illustrated in Fig. 5.27 for the MTBE synthesis where the rate has a negative order with respect to the educt methanol. 

r is the intrinsic reaction rate per volume of catalyst at liquid bulk conditions 

When formulating a microkinetic rate expression r(T,x) one has to account for the sorption equilibria of the reaction components between the liquid phase and the active catalyst phase. For this purpose, since the liquid-phase reaction mixtures have a strongly non-ideal behavior, one should use generalized Langmuir sorption isotherms in terms of liquid-phase activities as proposed first in the pioneer work of Rehfinger and Hoffmann [45]. According to these authors, the sorption equilibria of the N species A on one active site S is given by 

---