QUESTION

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Consider the reaction below for the production of benzene via homogeneous thermal dealkylation of the toluene in the temperature range of $700{ }^{\circ} \mathrm{C}$ to $950{ }^{\circ} \mathrm{C}$. \[ \begin{array}{l} \mathrm{C}_{7} \mathrm{H}_{8}+\mathrm{H}_{2} \rightarrow \mathrm{C}_{6} \mathrm{H}_{6}+\mathrm{CH}_{4} \\ -r_{\text {tol }}=3 \cdot 10^{10} e^{25,614 / T[K]} C_{T o l} C_{H_{2}}^{0.5}\left[\frac{\mathrm{mol}}{\mathrm{m}^{3}} \cdot \mathrm{s}\right] \\ \end{array} \] Where concentrations of reactants are in $\mathrm{mol} / \mathrm{L}$ reactor and the temperature is in $\mathrm{K}$. The heat of reaction is $-52.0 \mathrm{~kJ} / \mathrm{mol}\left(\right.$ at $900^{\circ} \mathrm{C}$ ) and $-50.5 \mathrm{~kJ} / \mathrm{mol}\left(\right.$ at $\left.700{ }^{\circ} \mathrm{C}\right)$, and the average specific heats of the reactor feed and effluent are $3.3216 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\left(\right.$ at $\left.950{ }^{\circ} \mathrm{C}\right)$ and $3.042 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\left(\right.$ at $\left.700{ }^{\circ} \mathrm{C}\right)$. a. If feed enters the reactor at $700{ }^{\circ} \mathrm{C}$ and $25 \mathrm{bar}$, solve the material and energy balances for a plug flow reactor to determine the volume of reactor needed to give $90 \%$ conversion of toluene. Do not use a process simulator for this portion The feed to the reactor comprises $80 \mathrm{kmol} / \mathrm{hr}$ of toluene and $320 \mathrm{kmol} / \mathrm{hr}$ of hydrogen. Plot the conversion and temperature profiles in the reactor versus reactor volume.

b) If the reactor above is packed with inert ceramic spheres with a diameter of 5 mm and a bed voidage of 0.45, determine the pressure drop across the reactor. Additionally, the reactor length-to-diameter ratio is now set to 8:1 and you can use an average process gas viscosity of 26.8·10-6 kg/m·s. Average gas density can be calculated using the ideal gas law.

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MHDUJK The First Answerer