Question $2$

a$.$ Briefly explain degree of freedom

$4$

b$.$ A natural gas processing plant is to separate natural gas into an ethane stream, a propane$/$i$-$butane stream, and a sales gas stream that is mainly methane. The natural gas feed rate is $2500kg.mo\frac{l}{h},$ and the composition is $83$mol$\%,12$mol$\%,4$mol$\%,$ and $1$mol$\%$ methane, ethane, propane, and $n-$butane, respectively. The ethane product stream contains $1$mol$\%$ methane, $2$mol$\%$ propane, and negligible butane. The propane product stream contains all the butane, $2$mol$\%$ ethane, and negligible methane. The sales gas contains $0\mathrm{.}5$mol$\%$ ethane, and the rest is methane. Calculate the flow rate of each product stream.

$6$

c$.$ Synthesis gas may be prepared by a continuous, noncatalytic conversion of any hydrocarbon by means of controlled partial combustion in a firebrick$-$lined reactor. In the basic form of this process, the hydrocarbon and oxidant $($oxygen or air$)$ are separately preheated and charged to the reactor. Before entering the reaction zone, the two feedstocks are intimately mixed in a combustion chamber. The heat produced by combustion of part of the hydrocarbon pyrolyzes the remaining hydrocarbons into gas and a small amount of carbon in the reaction zone. The reactor effluent then passes through a waste$-$heat boiler, a water$-$wash carbon$-$removal unit, and a water cooler$-$scrubber. Carbon is recovered in equipment of simple design in a form which can be used as fuel or in ordinary carbon products. Prepare a qualitative flowsheet for the process, showing all pieces of equipment.

$10$