CH EN 4253 Process Design Prof. T. A. Ring HW 11- Reactor Design Your objective is to design a reactor system for the production of 100 kmol/h cumene at 99% purity from benzene and propylene. The cumene can be sold for $0.275/lb while the benzene and propylene will cost $2.80/gal and $66/tonne, respectively. Please develop a reactor system in a process simulator of your choice and perform a full profitability analysis on the production of cumene using the reactor and separator information below. Reactor Information: The production of Cumene (AKA isopropyl benzene) is performed commercially by reaction of benzene with propylene. The examination of patents reveals that the reactor takes place between 150 and 230˚C and 25 and 35 bar(g) on zeolite catalyst ($2000/tonne) of small particle size (0.25-0.4 mm) with particle density of 1000 kg/m3, particle porosity, εp, of 0.5, bed void fraction, εb, of 0.2 and pore tortuosity, τp, of 5, where there are no diffusion and mass-transfer limitations. For these reaction conditions the benzene is a liquid trickling over the catalyst assumed to be a plug flow reactor for both the liquid and the gas phases. The surface reaction follows the Eley-Rideal mechanism in which the adsorption of propylene is predominant over benzene and the reaction takes place on the catalyst surface. The overall reaction can be effected by pore diffusion and external mass transfer so it should be build into the reaction rate expression in your simulation. The combination of resistances leads to the following first order apparent kinetic rate constant: k1,app=[(ηk1)-1+(kMTap)-1]-1 where η[=(3/ φ2)(φ/tanh φ-1)] is the catalyst effectiveness factor accounting for the diffusion and reaction internal to the catalyst particles which is determined from the Theile modulus, φ [=(dp/2)(k1/DP,eff)1/2]. The external mass transfer coefficient, kMT, can be calculated assuming the Sherwood number is 2.0 (corresponding to the small Reynolds number case). The specific mass-transfer area per unit bed volume, ap, depends upon the particle diameter, dp, and the bed porosity, εb, as follows: ap=(6/dp)(1- εb) The effective diffusion coefficient for propylene in the pores in the catalyst is given by: DP,eff = DP,Bulk.(εp/τp) in which DP,Bulk is the bulk diffusion coefficient, εp is the particle porosity and τp is the pore tortousity. The diffusion coefficient for propylene in benzene can be determined using the following temperature dependent formula: DP,Bulk= 2 x 10-3 (T/298K) cm2/s The desired reaction can be written as:CH EN 4253 Process Design Prof. T. A. Ring Benzene + propylene ÅÆ Cumene with a pseudo first order rate constant k1= 6.51e3 1/s exp(-52,564 kJ/kmol/RT). There is an undesired reaction which can be written as: Cumene + propyleneÅÆ Diisopropyl benzene with another pseudo first order rate constant k1= 4.5e2 1/s exp(-55,000 kJ/kmol/RT). The focus of your design should be on the operating conditions that will provide high conversion and high selectivity in as small as reactor as possible. The following issues should be addressed in your report and optimized in your design: feed ratio of reactants, reactor pressure and reactor temperature as well as heat management in the reactor. Your design report should focus on all aspects of reactor design as well as the economics of the total process. Separator Information: After the reactor the separation system will consist of a flash to produce un-reacted propylene as a vapor for recycle should it not be consumed by the reaction. The bottoms go next to a distillation column that is used to produce benzene overhead again for recycle. Finally the cumene is separated from Diisopropyl benzene in the last distillation column. Diisopropyl benzene is the bottom product and consists of a waste product without sales value. Assume clean separations. Do not design the separation system with its flash and two distillation but use the information provided below for their capital and operating costs. Capital Costs Bare Module Cost Flash $50,000 Distillation 1 $1,400,000 Distillation 2 $1,200,000 Cooling water utilization 250,000 gal/day Steam, 50 psig 200,000