In view of the expected long$-$term energy shortages, considerable effort is being expended to

develop processes for upgrading low$-$quality energy sources to high$-$quality fuels. The flowsheet

shown in the next page Figure is an example of such a scheme. In it$,$ high$-$sulfur coal, a fuel which

otherwise could not be used because of air quality standards, is gasified to produce a clean

synthetic natural gas $($SNG$).$ Powdered coal and steam per $1lb$ coal$)$ are charged to a

reactor which at high temperature and pressure produces a complex mixture of gases including

$10\%($mole basis$)$ methane. The heat for the reaction is provided by burning some of the charged

coal with oxygen introduced directly into the reactor. The raw product gas is cooled, treated for

removal of entrained ash, and sent to a second reactor, the shift converter. In this unit, the $H_2-$to$-$CO

mole ratio of $0\mathrm{.}56$:$1$ is increased by converting $62\mathrm{.}5\%$ of the $CO.$ The shifted gas, still containing

$10\%C{H}_4,$ is next treated for removal of the acid gases, $H_{2}S$ and $C{O}_2.$ Finally, the residual gas,

containing $49\mathrm{.}2\%H_2$ on an $H_{2}O-$free basis, is sent to a catalytic reactor which produces additional

methane. The final $H_{2}O-$free product gas contains $5\%H_2,0\mathrm{.}1\%CO,$ and the rest $C{H}_4($mole basis$).$

Calculate all flows in the process based on a feed of $10000l\frac{b}{h}$ coal and assuming $25\%$ of the

carbon fed ultimately appears in the product.