Review Problem #$5$

Butadiene is an important precursor in the production of synthetic rubber. One method of producing butadiene is the Houdry Catadiene process in which n$-$butane is dehydrogenated over a chromium $/$ alumina catalyst to yield butadiene and hydrogen. The reaction proceeds according the reaction shown below:

$C_4{H}_{10}{C}_4{H}_6+2H_2$

A schematic of the reaction is shown in Figure $1$ on page $2.$ The fresh feed $($stream $1)$ is composed of n$-$butane and is initially at $25C$ and $250$kPa. The n$-$butane is heated to $750C$ and fed into the reactor. The endothermic reaction proceeds to almost complete conversion $($you may assume $100\%$ conversion$).$ The products exiting the reactor $($stream $2)$ are at $20.$kPa and $650C.$ Stream $2$ is fed into a condenser in which it is cooled at constant pressure to $-50.C$ causing all the butadiene $($and none of the hydrogen$)$ to condense. This process will convert $15,000k\frac{g}{h}r$ of butane into butadiene. Please be aware that there is additional information on butadiene shown below. Determine the minimum duty $($i$.$e$.$ how much heat must be removed$)$ of the condenser. $(70$ points$)$

Butadiene constants:

$T_c=425K$

$P_c=\frac{43\mathrm{.}2}{b}ar$

$T_{\text{t}\text{r}\text{i}\text{p}\text{l}\text{e}}=164\mathrm{.}24K$

$T_b=268\mathrm{.}6K$

$MW=54\mathrm{.}09\frac{g}{m}ol$

Butadiene heat capacity constants $($where the temperature is in Celsius$)$:

Gas Liquid

$a=9\mathrm{.}125{10}^{-2},a=4\mathrm{.}237{10}^{-2}$

$b=2\mathrm{.}723{10}^{-4},b=2\mathrm{.}162{10}^{-4}$

$c=-1\mathrm{.}612{10}^{-7},c=0$

$d=3\mathrm{.}388{10}^{-11},d=0$

Butadiene Antoine constants $($for use with the following Antoine equation$)$

$lo{g}_{10}{P}^{\text{s}\text{a}\text{t}}=A-\frac{B}{T+C}$

Where $P^{\text{s}\text{a}\text{t}}$ is in bar and temperature is in Kelvin.

$A=3\mathrm{.}99798$

$B=941\mathrm{.}662$

$C=-32\mathrm{.}753$

$\{$Answer: around $12\mathrm{.}3$ or $12\mathrm{.}1MW$ depending on what thermodynamic path you choose$]$