Project $2$: FUG Method and HYSYS Simulation

Problem Statement

Please design a de$-$ethanizer to perform the separation illustrated in Figure $1.$ The five species in the feed with corresponding flow rates are methane $(C_1,160$kmo$\frac{l}{h}),$ etharte $(C_2,370$kmo$\frac{l}{h}),$ propane $(($:$C_3,240$kmo$\frac{l}{h}\},$ n$-$butane $(($:$n{C}_4,25$kmo$\frac{l}{h}\},$ and n$-$pentaneane $(n{C}_5,5$kmo$\frac{l}{h}).$ Use propane $C_3$ as the reference. The average relative volatilities of $C_1-$ nC $C_5$ relative to $C_3$ are, respectively, $8\mathrm{.}22,2\mathrm{.}42,1\mathrm{.}00,0\mathrm{.}378,0\mathrm{.}150.$ The desirable flow rate of $C_3$ in the distillate is $2$kmo$\frac{l}{h}.$ The expected flow of $C_2$ in the bottom is $2$kmo$\frac{l}{h}.$ The feed is saturated vapor. Complete the design of this column where design variables include the total number of actual stages, the compositions of distillate and bottoms, the optimum feed plate location, and the reflux ratio.

Figure $1.$ Light Ends De$-$ethanizer ${?}^{[1]}.$

$2.$ Tasks to be Completed and Presented in the Report

Task $1.$ With the given information in problem statement, $($a$)$ identify the light key $($LK$),$ heavy key $($HK$),$ light non key $($LNK$),$ and heavy non key $($HNK$)$; $($b$)$ compute the fraction recoveries $($FRs$)$ for the LK and HK$.$

Items to be included in your report: $(1)$ Specify all the LK$,$ HK$,$ LNK$,$ and HNK; $(2)$ Show the calculation procedures and results for FRs of LK and HK in both distillate and bottom.

Task $2.$ Use the Fenske equation to determine: $($a$)$ the minimum number equilibrium stages $N_{\text{m}\text{i}\text{n}}$; $($b$)$ the fractional recoveries for all non$-$keys in the distillate and bottom.

Items to be included in your report: $(1)$ Calculation procedures and results for $N_{\text{m}\text{i}\text{n}}$; $(2)$ Calculation procedures and results for FRs of all non$-$keys in both distillate and bottom.

Task $3.$ Using the obtained FRs for species in distillate and bottom from Tasks $1-2,$ show: $($a$)$ flow rates of each component in the distillate $D{x}_{i,\text{d}\text{i}\text{s}\text{t}}$ and bottom $B{x}_{i,\text{b}\text{o}\text{t}}$; $($b$)$ minimum reflux ratio $($L$/$D$)$