BalanceIn petroleum refining, hydrocracking is the catalytic splitting and addition of $H_2$ to large hydrocarbon molecules and the resultant production of smaller, more volatile, and more saturated molecules.

In the laboratory$-$scale testing of a new catalyst, the following process is run. Fresh fuel oil is fed to the process at a rate of $100\mathrm{.}0k\frac{g}{h}.$It is combined with a recycled oil stream, a fresh $H_2$ feed, and a recycled $H_2$ stream to enter a catalytic reactor in which hydrocracking occurs. The product stream from the reactor is fed to a gas separator in which unreacted $H_2$ gas is split off from the product stream and mixed with the fresh $H_2$ feed for the reactor. The liquid stream from the gas separator is fed to a fractionator which splits the stream into light and heavy fractions; the heavy fraction is recycled and mixed with the fresh heavy oil. The light fraction is collected as product and tested for suitability as a component of a gasoline$-$like fuel.

The molar ratios of atomic $\frac{H}{C}$ in the feed oil and in the light product are $1\mathrm{.}69$ and $2\mathrm{.}24$ respectively, and both are free of other atomic species.

The mass ratio of recycled oil to light product is $1\mathrm{.}55$ ; the molar ratio of $\frac{H}{C}$ in the recycled oil is $1\mathrm{.}87.$

The mass ratio of $H_2$ to oil fed to the reactor is $0\mathrm{.}0430.$

QUESTIONS: Draw and label a flow diagram and calculate the following quantities by analyzing the overall system.

Mass of light fuel produced: in kg$/$hr

Mass of $H_2$ fed to the process: in kg$/$hr