Reactor Type: Packed Bed Reactor PBR A packed bed reactor is suitable for this hydrogenation process because it allows for efficient contact between the reactants benzene and hydrogen and the catalyst, which is typically a metal such as palladium or platinum supported on an inert material like alumina. The PBR also provides good heat transfer and can handle the high operating pressure.Reactor Size and Parameters:1. Molar flow rates:Molecular weight of benzene C6H6 = 78 g/molMolecular weight of hydrogen H2 = 2 g/molBenzene flow rate = 900 kg/hr * 1000 g/kg / 78 g/mol = 11,538.5 mol/hrHydrogen flow rate = 3000 kg/hr * 1000 g/kg / 2 g/mol = 1,500,000 mol/hr2. Conversion and stoichiometry:90% conversion of benzene means 90% of the benzene fed to the reactor will be converted to cyclohexane.Converted benzene = 0.9 * 11,538.5 mol/hr = 10,384.65 mol/hrFrom the stoichiometry of the reaction, 1 mol of benzene reacts with 3 mol of hydrogen. Therefore, the required hydrogen for the reaction is:Required hydrogen = 10,384.65 mol/hr * 3 = 31,153.95 mol/hrSince the hydrogen flow rate is limited to 1,500,000 mol/hr, there is an excess of hydrogen available for the reaction.3. Residence time:Residence time is the time required for the reactants to stay in the reactor for the desired conversion. It can be estimated using the following formula:Residence time = reactor volume V / volumetric flow rate Q To estimate the reactor volume, we can use the following formula:V = k * * Q / 1 - X Where:k = reaction rate constant assumed to be 1 for simplicity X = conversion 0.9 We need to calculate the volumetric flow rate Q using the ideal gas law:PV = nRTWhere:P = pressure 20 atm V = volume unknown n = moles of benzene and hydrogen 11,538.5 + 1,500,000 mol/hr R = gas constant 0.0821 L atm/mol K T = temperature 300C + 273.15 = 573.15 K Rearranging the ideal gas law to solve for volume:V = nRT / PV = 11,538.5 + 1,500,000 * 0.0821 * 573.15 / 20 = 2,324,131.6 L/hrNow we can calculate the residence time : = 1 * 2,324,131.6 / 1 - 0.9 = 23,241,316 L4. Heat transfer and pressure drop:Heat transfer is essential to maintain the reactor temperature at 300C. The packed bed reactor can be designed with cooling jackets or heat exchangers to remove the heat generated during the exothermic hydrogenation reaction.The pressure drop across the packed bed reactor should be minimized to ensure efficient operation. This can be achieved by optimizing the catalyst particle size, bed height, and reactor diameter. The Ergun equation can be used to estimate the pressure drop and design the reactor accordingly.In conclusion, a packed bed reactor with a volume of 23,241,316 L and operating at 300C and 20 atm can be designed to achieve 90% conversion of benzene to cyclohexane with a benzene flow rate of 900 kg/hr and a hydrogen flow rate of 3000 kg/hr. The reactor should be designed with efficient heat transfer and minimized pressure drop for optimal performance.