The following table presents residual heat flows in the enthalpy cascade of a process computed at \(\Delta T_{\text {min }}=10^{\circ} \mathrm{C}\) (Smith, 2005):

(a) It is desired to efficiently heat integrate a distillation column for the separation of a binary mixture of toluene and biphenyl with this process. The column produces essentially pure product streams and is originally designed to operate at 1.013 bar. At that pressure, toluene boils at \(107^{\circ} \mathrm{C}\), and biphenyl at \(197^{\circ} \mathrm{C}\). The condenser and reboiler duties are both \(4 \mathrm{MW}\). What will be the consequences of attempting to heat integrate the column operating at 1.013 bar?

(b) What is your recommendation for an appropriate operating pressure for the column, assuming that the condenser and reboiler duties as stated above are independent of operating pressure and that vapor pressure of toluene and biphenyl are estimated using the Antoine equation:
\[\ln P_{i}=A_{i}-\frac{B_{i}}{T+C_{i}}\]
where \(P_{i}\) is the vapor pressure (bar), \(T_{i}\) is the temperature (K), and the remaining parameters are listed in the following table. The selection of operating pressure should be made to maintain the reboiler temperature as low as possible while avoiding operation in vacuum conditions.
Parameter values for Antoine equation:

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Interval Temperature (C) 295 285 Residual Heat Flow (MW) 18.3 19.8 4.8 185 145 85 45 0 10.8 12.0 35 14.3