P5-148 The dehydration butanol of alumina is carried out over a silica-alumina catalyst at 680 K.
$CH_3CH_2CH_2CH_2OH \rightarrow CH_3CH=CHCH_3 + H_2O$
The rate law is
$-r_{Bu} = \frac{kP_{Bu}}{(1 + K_{Bu}P_{Bu})^2}$
with $k = 0.054$ mol/gcat·hatm and $K_{Bu} = 0.32$ atm?¹. Pure butanol enters a thin-tubed, packed-bed
reactor at a molar flow rate of 50 kmol/hr and a pressure of 10 atm (1013 kPa).
(a) What PBR catalyst weight is necessary to achieve 80% conversion in the absence of pressure
drop? Plot and analyze $X$, $p$, $f$ (i.e., $(v/v_0)$) and reaction rate, $-r_k$, as a function of catalyst weight.
(b) What \"fluidized CSTR\" catalyst weight is necessary to achieve 80% conversion?
(c) Repeat (a) when there is pressure drop, with the pressure-drop parameter $\alpha = 0.0006$ kg?¹. Do you
observe a maximum in the rate of reaction, and if so, why? What catalyst weight is necessary to
achieve 70% conversion? Compare this weight with that for no pressure drop to achieve the same
conversion.
(d) What generalizations can you make about this problem?