A trim heater is to be designed to heat \(116,000 \mathrm{lb} / \mathrm{hr}\) of \(57 \mathrm{wt} \%\) ethane, \(25 \mathrm{wt} \%\) propane, and \(18 \mathrm{wt} \%\) n-butane from 80 to \(96^{\circ} \mathrm{F}\). The stream will enter the exchanger at 520 psia and must not reach the bubble point in the exchanger. The stream will be heated with gasoline, which will enter at \(240^{\circ} \mathrm{F}\) and \(95 \mathrm{psia}\), with a flow rate of \(34,000 \mathrm{lb} / \mathrm{hr}\). Standard practice of the company is to use 1-2 shell-and-tube heat exchangers with 3/4-in., 16 BWG carbon steel tubes, \(20 \mathrm{ft}\) long, 1 -in. square pitch. Tube count depends on shell diameter, with the following diameters available:

The gasoline will flow on the shell side. Assume a combined fouling factor of 0.002 (hr-ft²-^∘F)/Btu. Design a suitable heat exchange system, assuming a 25% overdesign factor.

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Shell I.D. (in.) Tube Count 10 52 12 78 13.25 96 15.25 136 17.25 176 19.25 224