Zeroth-order kinetics catalytic reactor

Thus, with the usual experimental procedures, a comparison of conversion data as a function of space velocity (residence time) does not tell us whether the kinetics differ from first order in the region of conversion below 50% for the range of order tested (zeroth to second). On the contrary, first-order kinetics can be used to represent the conversion as a function of residence time for a wide range of situations. Some investigators have been aware of this approximate first-order behavior of integral reactors, as shown by the statement that even complex catalytic systems approximate a pseudo- first order relationship when only space velocity is varied. .. (10). 

The mass balance with homogeneous one-dimensional diffusion and irreversible nth-order chemical reaction provides basic information for the spatial dependence of reactant molar density within a catalytic pellet. Since this problem is based on one isolated pellet, the molar density profile can be obtained for any type of chemical kinetics. Of course, analytical solutions are available only when the rate law conforms to simple zeroth- or first-order kinetics. Numerical techniques are required to solve the mass balance when the kinetics are more complex. The rationale for developing a correlation between the effectiveness factor and intrapellet Damkohler number is based on the fact that the reactor design engineer does not want to consider details of the interplay between diffusion and chemical reaction in each catalytic pellet when these pellets are packed in a large-scale reactor. The strategy is formulated as follows ... 

For a particular experiment in a packed catalytic tubular reactor, the chemical kinetics can be approximated by a zeroth-order rate law where the best value for the zeroth-order rate constant is calculated via the formalism on pages 459 and 460. At what value of the intrapeUet Damkohler number Aa. intrapellet does reactant A occupy 75% by volume of the catalyst if the porous pellets are (a) spherical, (b) long cylinders, and (c) wafer-like ... 

At high-mass-transfer Peclet numbers, sketch the relation between average residence time divided by the chemical reaction time constant (i.e., r/co) for a packed catalytic tubular reactor versus the intrapeUet Damkohler number Aa, intrapeiiet for zeroth-, first-, and second-order irreversible chemical kinetics within spherical catalytic pellets. The characteristic length L in the definition of Aa, intrapeiiet is the sphere radius R. The overall objective is to achieve the same conversion in the exit stream for all three kinetic rate laws. Put all three curves on the same set of axes and identify quantitative values for the intrapeiiet Damkohler number on the horizontal axis. 

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