Chemical Engineering Kinetics. J$.$M$.$ Smith

$13\mathrm{.}7$ InIn order to compare different batches of catalysts for fixed$-$bed cracking operations it is desired to develop a numerical catalyst activity by comparing each batch with a so$-$called "standard catalyst" for which the $x-$vs$-$W$/$F curve is known. If the activity of a batch is defined$\_$as the$\_$rate of reaction of that batch divided by the rate for the standard catalyst at the same conditions, which of the following two procedures would be the better measure of catalyst activity?

$($a$)$ Determine from the curves the values of $\frac{W}{F}$ required to obtain the same conversion $x,$ and call the activity the ratio

$\frac{(\frac{W}{F}{)}_{standard}}{(\frac{W}{F}{)}_{\text{a}\text{c}\text{t}\text{u}\text{a}\text{l}}}$

$($b$)$ Determine from the curves the values of $x$ at the same $\frac{W}{F},$ and define the activity as

$\frac{x_{\text{a}\text{c}\text{t}\text{u}\text{a}\text{l}}}{x_{standard}}$

Sketch the $x-$vs$-\frac{W}{F}$ curve for a standard catalyst and a curve for a catalyst with an activity less than unity. order to compare different batches of catalysts for fixed$-$bed cracking operations it is desired to develop a numerical catalyst activity by comparing each batch with a so$-$called "standard catalyst" for which the x$-$vs$-$W$/$F curve is known. If the activity of a batch is defined$\_$as$\_$the$\_$rate of reaction of that batch divided by the rate for the standard catalyst at the same conditions, which of the following two procedures would be the better measure of catalyst activity?

$($a$)$ Determine from the curves the values of W$/$F required to obtain the same conversion x$,$ and call the activity the ratio

$($W$/$F$)$ standard$/($W$/$F$)$actual

$($b$)$ Determine from the curves the values of x at the same W$/$F$,$ and define the activity asXactualXstandardSketch the x$-$vs$-$W$/$F curve for a standard catalyst and a curve for a catalyst with an activity less than unity.