Ammonia synthesis kinetic model

D.A. Rudd, L.A. Apuvicio, J.E. Bekoske and A.A. Trevino, The Microkinetics of Heterogeneous Catalysis (1993), American Chemical Society, Washington DC]. Ideally, as many parameters as can be determined by surface science studies of adsorption and of elementary steps, as well as results from computational studies, are used as the input in a kinetic model, so that fitting of parameters, as employed in Section 7.2, can be avoided. We shall use the synthesis of ammonia as a worked example [P. Stoltze and J.K. Norskov, Phys. Rev. Lett. 55 (1985) 2502 J. Catal. 110 (1988) Ij. 

The first step in constructing a micro-kinetic model is to identify all the elementary reaction steps that may be involved in the catalytic process we want to describe, in this case the synthesis of ammonia. The overall reaction is... 

The elementary steps in the kinetic model for ammonia synthesis are ... 

The kinetics of the ammonia synthesis have been discussed as an example of micro-kinetic modeling in Chapter 7. Here we present a brief description of the process, concentrating on how process variables are related to the microscopic details and the optimization of the synthesis. 

An analysis of this equation shows that, as in the case of ammonia synthesis, the maximum conversion rate at any point of the reactor can only be achieved by establishing a temperature gradieiiL This must be supplemented by the analyris of the kinetics relative to the reverse reaction of CO shift conversion. The models that can be constructed on the basis of published experimental results show that, wift catalysts based on cof icr... 

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) ... 

Ammonia concentration calculated from microkinetic model versus longitudinal distance from reactor inlet. (Figure adapted from Kinetic Simulation of Ammonia Synthesis Catalysis by J. A. Dumesic and A. A. Trevino, in Journal of Catalysis, Volume 116 119, copyright 1989 by Academic Press, reproduced by permission of the publisher and the authors.)... 

P. Stoltze and J.K. Norskov, An interpretation of the high-pressure kinetics of ammonia synthesis based on a microscopic model. /. Catal. 110,1 (1988). 

Buzzi Ferraris et al. (1974) use the mathematical analysis of kinetic data to build rate equations for the ammonia synthesis reaction. They offer more than 20 models which give good fitting of experimental data. 

Widely used kinetic models for industrial ammonia synthesis... 

In the kinetic modelling of catalytic reactions, one typically takes into account the presence of many different surface species and many reaction steps. Their relative importance will depend on reaction conditions (conversion, temperature, pressure, etc.) and as a result, it is generally desirable to introduce complete kinetic fundamental descriptions using, for example, the microkinetic treatment [1]. In many cases, such models can be based on detailed molecular information about the elementary steps obtained from, for example, surface science or in situ studies. Such kinetic models may be used as an important tool in catalyst and process development. In recent years, this field has attracted much attention and, for example, we have in our laboratories found the microkinetic treatment very useful for modelling such reactions as ammonia synthesis [2-4], water gas shift and methanol synthesis [5,6,7,8], methane decomposition [9], CO methanation [10,11], and SCR deNO [12,13]. 

M. Bowker, 1. Parker, and K.C. Waugh. Extrapolation of the Kinetics of Model Ammonia Synthesis to Industrially Relevant Temperatures and Pressures. Appl. Catal. 14 101 (1985). 

In addition to the skeptic s view of LH correlations, however, there must be additional reasons why this model has been used successfully for the correlation of kinetics in so many different types of catalytic reactions. Two factors seem to be most important. First is the fact that the expressions are fairly insensitive to the precise sort of kinetic scheme involved. Many widely differing types of reaction sequences can be shown to give approximate LH forms, as given in Tables 3.2 and 3.3 [see also a further good example based on the ammonia synthesis reaction by G. Buzzi Ferraris, G. Donati, F. Rejna and S. Carra, Chem. Eng. Sci., 29, 1621 (1974)]. Second is the fact that for reasonable assumptions concerning the nature of typical nonuniform surfaces it can be shown that they tend to look like uniform surfaces in overall behavior. This second point can be illustrated by an example scheme in which the heat of formation of surface complexes is a linear function of surface coverage. Consider the two-step sequence... 

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