Nitrogen effective diffusivity

Results were surprising. By getting Def > 0 D, i.e., the effective diffusivity of ethane in nitrogen was larger than predicted by the formula of... 

In this exercise we shall estimate the influence of transport limitations when testing an ammonia catalyst such as that described in Exercise 5.1 by estimating the effectiveness factor e. We are aware that the radius of the catalyst particles is essential so the fused and reduced catalyst is crushed into small particles. A fraction with a narrow distribution of = 0.2 mm is used for the experiment. We shall assume that the particles are ideally spherical. The effective diffusion constant is not easily accessible but we assume that it is approximately a factor of 100 lower than the free diffusion, which is in the proximity of 0.4 cm s . A test is then made with a stoichiometric mixture of N2/H2 at 4 bar under the assumption that the process is far from equilibrium and first order in nitrogen. The reaction is planned to run at 600 K, and from fundamental studies on a single crystal the TOP is roughly 0.05 per iron atom in the surface. From Exercise 5.1 we utilize that 1 g of reduced catalyst has a volume of 0.2 cm g , that the pore volume constitutes 0.1 cm g and that the total surface area, which we will assume is the pore area, is 29 m g , and that of this is the 18 m g- is the pure iron Fe(lOO) surface. Note that there is some dispute as to which are the active sites on iron (a dispute that we disregard here). 

The measured effective diffusivities are those of hydrogen in nitrogen at room temperature and pressure except that of Haldor Topsoe which is of helium in nitrogen. 

He Pulses in Nitrogen Figure 1. illustrates a typical response curve (continuous line) obtained for a 1 second pulse of He in a nitrogen carrier gas stream. Using the moment method (12), the effective diffusion coefficient for He is 0.137 cm /sec. To compare this with steady state data, it is necessary to make use of equation (3). 

Results. For O3, experiments were made with both nitrogen and helium as carrier gas in the pressure range of 29 to 85 torr, covering an effective diffusivity range of 1.46 to 5.61 cm /sec. Data were taken at three different temperatures, namely, 0, 10 and 19°C. The effects of added chemical reagent on the apparent accommodation coefficient,... 

Let us illustrate the calculation of the effective diffusivity and the molar fluxes for the conditions existing at the start of the two bulb diffusion cell experiment of Duncan and Toor discussed in Examples 5.3.1 and 5.4.1. The components are hydrogen (1), nitrogen (2), and carbon dioxide (3) and the values of the diffusion coefficients of the three binary pairs at 35.2° C and 1-atm pressure were... 

The flux of hydrogen (component 1) is not too different from the flux estimated using the linearized equations in Example 5.3.1. However, the effective diffusivity method predicts a very small flux of nitrogen (component 2), a result quite different from the predictions of the linearized theory. This, of course, is because the effective diffusivity method ignores the contribution due to the driving forces of the other components. We will investigate the consequences of this prediction in Example 6.4.1. ... 

Figure 6.1 shows the concentration time history in the diffusion cell for the experiment of Duncan and Toor that was described in detail in Example 5.4.1. The mole fraction of hydrogen predicted by the effective diffusivity model compares well with the experimental data of Duncan (1960). However, the effective diffusivity model suggests that the mole fraction of nitrogen should remain almost constant at approximately 0.5. This is in stark contrast to the experimental data (Fig. 6.1). The results obtained with the effective diffusivity method for nitrogen are completely different from those obtained with the linearized theory. Additional comparisons between the data of Duncan and Toor and the predictions of both the linearized equations and the effective diffusivity models are shown in the triangular diagram in Figure 6.2.

It is worth noting that the almost constant value of the composition of nitrogen would have been predicted with any of the formulas used in Example 6.1.1 to calculate the effective diffusivity. Thus, we have our first demonstration of the inability of the effective diffusivity approach to model multicomponent diffusion processes. ... 

The results in Table 6.7, 6.8 show that although the effective diffusivity of hydrogen predicted by the Stefan-Maxwell equation is higher than that of the Wilke equation (Table 6.8), the opposite is true for nitrogen and ammonia and the final outcome is that the simulation results are almost the same (Table 6.7), and there is no significant difference between the results of the two equations, especially at the outlets of the second and third beds. However, a 2°C difference is observed at the outlet of the first bed, and at this point, the simplified... 

Ammonia is being absorbed from a stagnant mixture of nitrogen and hydrogen by contact with a 2 N sulfuric acid solution. At one place in the apparatus where the pressure is 1 bar and the temperature 300 K, the analysis of the gas is 40% NH3 (1), 20% N2 (2), and 40% H2 (3) by volume. Estimate the effective diffusivity of ammonia in the gaseous mixture. 

Calculate the effective diffusivity of nitrogen through a stagnant gas mixture at 400 K and 1.5 bar. The mixture composition is... 

A mechanism for the acceleratory stage based on the catalytic effect of colloidal lead particles would agree with the model used to explain photolysis of alkali azides. Hall and Williams showed that metal films in contact with lead azide alter the photodecomposition efficiency [96]. Alernatively, the acceleratory stage may result from an increased concentration of trapped nitrogen molecules diffusing to the surface. The deceleration is thought to result from a depletion of azide molecules in the near-surface regions [120]. 

The dusty-gas model offers an accurate way to estimate the effectiveness factor, concentration profiles, rates and instantaneous selectivities in a porous catalyst particle. The assumption of considering only one effective diffusion in nitrogen leads to an important overestimation in the reaction selectivity. Under the conditions studied here, high temperatures and low pressures favor the production of styrene. 

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