A$+$B$+$C$+$D elements react in the gas phase in an SSTR with a diameter of $0\mathrm{.}5$ m at constant temperature. The rate constant is k$=1\mathrm{.}0$ dm$/$mol$.$s$,$ and the volumetric flow rate is vo$=10$ dm$/$s$.$ The feed is stoichiometric in A and B$.$ The feed concentration of A is $0\mathrm{.}5$ mol$/$dm$.100$ kg of catalyst is used in the reactor. The catalyst decay law is first$-$order with kd$=0\mathrm{.}2$ s$.$

a$)$ Determine the conversion achieved in a reactor with a height of $10$ m$.$ Assume that the catalyst moves at the same speed as the gas in the reactor. Draw the X$-$Z graph.

b$)$ Determine the conversion achieved in a reactor with a height of $100$ m$.$ Assume that the catalyst moves at the same speed as the gas in the reactor. Draw the X$-$Z graph.

c$)$ What is the activity of the catalyst at the reactor outlet? Draw the A$-$Z graph.

d$)$ Considering reactor fixed and operating costs, what would be the optimal reactor size? Why?

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