Chapter 9, Problem 9.33P

Ethylbenzene is converted to styrene in the catalytic dehydrogenation reaction C«H₁₀(g) - $C_8{H}_{10}\left(g\right)\to C_8{H}_8\left(g\right)+H_2:\Delta H_r^{°}\left(600°C\right)=+124.5kJ$

A flowchart of a simplified version of the commercial process is shown here.

Fresh and recycled liquid ethylbenzene combine and are heated from 25°C to 500°C (A). and the heated ethylbenzene is mixed adiabatically with steam at 700°C (B) to produce the feed to the reactor at 600°C. (The steam suppresses undesired side reactions and removes carbon deposited on the catalyst surface.) A once-through conversion of 35% is achieved in the reactor (C), and the products emerge at 560°C. The product stream is cooled to 25°C (D), condensing essentially all of the water, ethylbenzene, and styrene and allowing hydrogen to pass out as a recoverable by-product of the process.

The water and hydrocarbon liquids are immiscible and are separated in a settling tank decanter (£). The water is vaporized and healed (F) to produce the steam that mixes with the ethylbenzene feed to the reactor. The hydrocarbon stream leaving the decanter is fed to a distillation tower(C) (actually, a series of towers), which separates the mixture into essentially pure styrene and ethylbenzene, each at 25°C after cooling and condensation steps have been carried out. The ethylbenzene is recycled to the reactor preheater, and the styrene is taken off as a product.

1. On a basis of 100 kg/h styrene produced, calculate the required fresh ethylbenzene feed rale, the flow rate of recycled ethylbenzene, and the circulation rate of water, all in mol/h. (Assume P = 1 atm.)
2. Calculate the required rates of heat input or withdrawal in kJ/h for the ethylbenzene preheater (A), steam generator (F), and reactor (C).

Suggest possible ways to improve the energy economy of this process.

Physical Property Data

   $\begin{array}{l}Ethylbenzene:{\left(C_p\right)}_{liquid}=182J/\left(mol\cdot °C\right)\\ \left(\Delta {\hat{H}}_v\right)=36.0kJ/molat136°C\\ {\left(C_p\right)}_{vapor}\left[J/\left(mol\cdot °C\right)\right]=118+0.30T\left(°C\right)\\ Styrene:{\left(C_p\right)}_{liquid}=209J/\left(mol\cdot °C\right)\\ \left(\Delta {\hat{H}}_v\right)=37.1kJ/molat145°C\\ {\left(C_p\right)}_{vapor}\left[J/\left(mol\cdot °C\right)\right]=115+0.27T\left(°C\right)\end{array}$