FUG Method! We are separating a multicomponent hydrocarbon feed with components given in the table below $($listed in order of decreasing volatility$)$ which is typical of the feed to the recovery section of an alkylation plant in a petroleum refinery. There are several schemes for the processing, and let's consider an approach with the first step being a debutanizer. The feed enters as a saturated liquid and the product specifications are that $99\mathrm{.}0\%$ of the n$-$butane goes to the overhead and the $64\%$ of the i$-$pentane goes to the bottoms product. Assume Raoult's Law and Dalton's Law are valid and use the Antoine equation parameters below$\mathrm{.}1$ Antoine Equation: log $10$ Pup $($bar$)=$ A T$($K$)+$C Antoine Equation Parameters Feed lbmol$/$hr $12\mathrm{.}0448\mathrm{.}036\mathrm{.}015\mathrm{.}023\mathrm{.}039\mathrm{.}1$ Compound $4\mathrm{.}32814\mathrm{.}355761175\mathrm{.}5813\mathrm{.}971831021\mathrm{.}8643\mathrm{.}98924\mathrm{.}002664\mathrm{.}028321268\mathrm{.}6364\mathrm{.}048671355\mathrm{.}1263\mathrm{.}824891492\mathrm{.}9281132\mathrm{.}1080\mathrm{.}9182\mathrm{.}071-43\mathrm{.}231-$butane $($iC$4)$ n$-$butane $($nC$4)-$pentane $($iC$5)$ n$-$pentane $($nC$5)$ n$-$hexane $($C$6)$ n$-$heptane $($C$7)$ n$-$octane $($C$8)$ n$-$nonane $($C$9)1070\mathrm{.}617-40\mathrm{.}454-48\mathrm{.}78456\mathrm{.}19963\mathrm{.}633-55\mathrm{.}8951171\mathrm{.}53272\mathrm{.}231\mathrm{.}0$ Specify splits for the two key components and estimate the splits for the nonkey components. Identify the light key $($LK$)$ and heavy key $($HK$)$ for this separation Calculate the key component flow rates in the distillate and bottoms products based on the separation specifications above. Generate preliminary estimates for the nonkey component splits $($i$.$e$.$ the flow rates in the distillate and bottoms products$)$ by assuming any component lighter than LK partitions entirely to the distillate and any component heavier than HK partitions entirely to the bottoms product. a$.$ Report your results as a table where the first column is the component $($in order of decreasing volatility$),$ the second column are the component flow rates in the feed, the third column are the component flow rates in the distillate, and the fourth column are the component flow rates in the bottoms product.