Industrial rates and the scale-down problem

In the catalyst particle, the steam reforming reaction approaches chemical equilibrium, where all reactions become first order in their limiting component. This implies that a simplified intrinsic rate equation may be written as the following function of the distance to equilibrium [389]  

It is convenient to insert the ratio P between the reaction quotient, Qr, and equilibrium constant as an approximation for the ratio between the equilibrium and actual CH4 concentrations  

At equilibrium p is exactly equal to unity. The rate equation can then be written as  

P is also related to the temperature approach to equilibrium. This can be seen when approximating the equilibriiun constant by ln(Keq)=A-B/Teq and similarly ln(Qr) A-B/T (B is positive). The resulting equations can be written as  

If Equation (3.5) is simplified to the one-dimensional model by neglecting the radial concentration gradient and a constant gas density 

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