Wilke equation

This equation reduces to Wilke equation, when it is used with the zero flow rates for k = 2, 3. 

The diffusion of species s in a multicomponent mixture can then be written in the form of Pick s law of binary diffusion, using the effective diffusion coefficient Dsrn instead of the binary diffusivity. The Wilke equation is defined by ... 

However, the Wilke equation does not in general satisfy the constraint that the species mole fractions must sum to 1 [14]. 

The mass diffusion flux may alternatively be calculated in accordance with the approximate Wilke equation (2.409). In this case the species mass balance reduces to ... 

The bulk diffusion processes within the pores of catalyst particles are usually described by the Wilke model formulation. The extended Wilke equation for diffusion in porous media reads ... 

Solving this flow model for the velocity the pressure is calculated from the ideal gas law. The temperature therein is obtained from the heat balance and the mixture density is estimated from the sum of the species densities. It is noted that if an inconsistent diffusive flux closure like the Wilke equation is adopted (i.e., the sum of the diffusive mass fluxes is not necessarily equal to zero) instead, the sum of the species mass balances does not exactly coincide with the mixture continuity equation. 

The multicomponent diffusivities are generally calculated from the Wilke equation, t represents the tortuosity factor for the pellet. 

The Ilux can be expressed by the Fiekian type dillusion ociiialion complemented by the simplified Wilke equation (Mahfouz, 1985) for the dependence of the diffusivities on the gas mixture composition. Following some lengthy but straightforward manipulation of the equations, the following equations are obtained (Mahfouz, 1985) for the intraparticle mole fraction profiles for any component ... 

Then Amis used in equation 181 to calculate Df. Of course this Wilke equation is strictly valid for dilute systems, but can be used as approximation for multicomponent systems. 

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... 

Wilke equation gives better (as compared with the experimental results) temperature prediction than the Stefan-Maxwell equation, but the conversion of the latter almost coincides with the experimental results. The use of the Stefan-Maxwell equation gives a slightly lower effectiveness factor along the reactor length. From the results it seems that the simplified equation of Wilke is quite satisfactory in this case. However, since the Stefan-Maxwell equation is the more rigorous, and its use in this case does not add any extra complications, it is the recommended method. 

As described in section 2, first task to tackle in this approach is to solve Wilks equation for fixed values of coverage level, confidence level, mnnber of hmits and dimension of the output, to find the minimum number of runs in a sample to achieve the selected levels. In this case... 

The approximate multi-component molecular diffusion coefficients were computed by use of the Wilke equation [165] ... 

The multicomponent diffusivities are generally calculated from the Wilke equation, the Maxwell-Stefan model or the dusty gas model. The diffusion flux models are outlined in Chap. 2 and further investigated by Solsvik and Jakobsen [15] and Solsvik et al. [17]. T represents the tortuosity factor for the pellet. 

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