$(20$ points$)$ Problem $4.$

The CRE algorithm equations are required. The numerical solution in Polymath, Matlab or Python is optional.

The liquefaction of Kentucky Coal No$.9$ was carried out in a slurry reactor $[$D$.$ D$.$ Gertenbach, R$.$ M$.$ Baldwin, and R$.$ L$.$ Bain. Ind. Eng. Chem. Process Des. Dev, $21,490(1982)\}.$ The coal particles, which were less than $200$ mesh, were dissolved in a $-250C$ vacuum cut of recycle oil saturated with hydrogen at $400C.$ Consider the reaction sequence

which is a modified version of the one given by Gertenbach et al$.$ All reactions are first order. Calculate the molar flow rate of each species as a function of space time in

$($a$)$ A plug$-$flow reactor.

$($b$)$ A $3-m^3$ CSTR$.$