Project $2$: FUG Method and HYSYS Simulation

$1.$ 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$1,160$ kmol$/$h$),$ ethane $($C$2,370$ kmol$/$h$),$ propane $($C$3,240$ kmol$/$h$),$ n$-$butane $($nC$4,25$ kmol$/$h$),$ and n$-$pentaneane $($nC$5,5$ kmol$/$h$).$ Use propane C$3$ as the reference. The average relative volatilities of C$1-$nC$5$ 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 $2$ kmol$/$h$.$ The expected flow of C$2$ in the bottom is $2$ kmol$/$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$\_$min; $($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$\_$min; $(2)$ 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 Dx$\_($i$,$dist$)$ and bottom Bx$\_($i$,$bot$)$; $($b$)$ minimum reflux ratio $($L$/$D$)$min from the Underwood equation.

Items to be included in your report: $(1)$ Calculation procedures and results for each Dx$\_($i$,$dist$)$ and Bx$\_($i$,$bot$)$; $(2)$ Calculation procedures and results for solving the $1$st and $2$nd Underwood equation to obtain Vmin, Lmin, D$,$ and $($L$/$D$)$min$.$

Task $4.$ Based on the results from Task $3,$ assume that the actual reflux ratio is L$/$D $=1\mathrm{.}25($L$/$D$)$ min. Determine: $($a$)$ the number N of stages required under the given actual reflux ratio; $(2)$ the optimum feed plate location NF$.$

Items to be included in your report: $(1)$ Calculation procedures and results for obtaining N $[$hint: follow the lecture example: obtain abscissa$,$ find Liddle correlation, determine the ordinate value, and then calculate N$]$; $(2)$ Calculation procedures and results for the optimum feed location NF$.$