Ammonia reaction kinetics Effectiveness factor

Mathematical models [216] for calculating these effectiveness factors involve simultaneous differential equations, which on account of the complex kinetics of ammonia synthesis cannot be solved analytically. Exact numerical integration procedures, as adopted by various research groups [157], [217]-[219], are rather troublesome and time consuming even for a fast computer. A simplification [220] can be used which can be integrated analytically when the ammonia kinetics are approximated by a pseudo-first-order reaction [214], [215], [221], according to the Equation (21) ... 

As examined in Section 4.5.4, the effectiveness factor is only constant and independent of the degree of conversion if we have an irreversible first-order reaction (Tab. 4.5.5, Example 4.5.6). This is not the case for NH3 synthesis, which is with regard to the kinetics much more complicated as we have a reversible nth order reaction according to the Eqs. (6.1.9) and (6.1.10). Hence, the effectiveness factor depends on the reactant (H2 and N2) and product (NH3) concentrations and thus on the axial position in a fixed bed reactor. This leads to a decrease of the intrinsic rate along the bed (at almost constant effective diffusion coefficients), and in return to an increase of the effectiveness factor from the reactor inlet to the outlet as shown in Figure 6.1.7 for an isothermal and therefore hypothetical ammonia reactor apart from the assumption of isothermality, the parameters used for the calculations correspond to an industrial reactor. 

As will be described in the section on kinetics, the rate of ammonia synthesis is a function of the rate of N2 chemisorption, the amount of adsorbed nitrogen (retardation), and the amount of adsorbed hydrogen (retardation). These factors in turn depend on the reaction conditions (temperature, pressure and flow rate) and the nature of the element. Thus, we might change the reaction rate or kinetics on a new active center which is composed of two elements (ensemble effect). A support and a promoter also influence such characteristics and will be described in the next section. However, if an alloy is used as a starting material, and the two elements are separated and turned into an active metal and an inert oxide, then the resulting activity should be classified as a support effect. 

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