Problem $1-9$ points

A demethanizer is the first tower in a natural gas processing plant and operates at high pressure and low temperature. The tower produces a residue gas as the top product and a Y$-$Grade NGL as the bottom product. Additionally, the tower has two side heat exchangers to help distribute the heat input and balance the vapor$/$liquid traffic in the column.

The preliminary design indicates that the feed $)=(1\mathrm{.}042Bt\frac{u}{b_m}F$ needs to be cooled from $80F$ to $-56F.$ In order to minimize the capital and operating costs of the refrigeration system, we will use the following process streams to cool the feed.

$\backslash$table$[[,T_{stan}(F{)}_{?},T_{\text{f}\text{i}\text{n}\text{i}\text{s}\text{h}}(F{)}_{?},\backslash$table$[[$Mass Flow$],[$Rate $(l\frac{b_m}{h}r)$