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Our packed bed reactor runs the gas phase reaction ARA \rightarrow \mathrm{R} at 10 atm and 336C,336^{\circ} \mathrm{C}, and gives 90% conversion of a pure A feed. However, the catalyst salesman guarantees that in the absence of any pore diffusion resistance our reaction will proceed on his new improved porous catalyst (De=2×106m3/m cat s)\left(\mathscr{D}_{e}=2 \times 10^{-6} \mathrm{m}^{3} / \mathrm{m} \text { cat } \cdot \mathrm{s}\right) with a rate given by rA=0.88CAmolm3cats-r_{\mathrm{A}}^{\prime \prime \prime}=0.88 C_{\mathrm{A}} \frac{\mathrm{mol}}{\mathrm{m}^{3} \mathrm{cat} \cdot \mathrm{s}} which is much better than what we now can do. The catalyst is rather expensive, since it is formulated of compressed kookaburra droppings and it is sold by weight. Still, we'll try it when we next replace our catalyst. What diameter of catalyst balls should we order?

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Answered 2 years ago
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To be most effective reaction we take the default amount MT0.4M_{T}\cong 0.4 which formula we use because there is already given the effective diffusion coefficient De\mathfrak {D_{e}}

MT=LkmDeM_{T}=L\sqrt{ \frac{k^{m}}{\mathfrak{D_{e}}}}

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