please help
Problem 2 [35 pts] You are a newly hired engineer working at an industrial facility which produces a waste containing stream including an environmentally hazardous waste A dissolved in water. This waste stream contains waste component A with a concentration of 10 g/m and is discharged from the facility with a constant total volumetric flow rate of 60 m/min. This stream is used to be sent into a river causing crucial hazards to ecosystem. New environmental regulations are made so that this waste stream, now, has to be treated using a steady state CSTR or a steady state PFR before being discharged into the river to reduce its harmful effects. New regulations state that a reactor should be used to treat this waste and outlet stream exiting the reactor should reach to 5% of its initial inlet concentration value, so that the stream will be safe for dumping into the river. You are the engineer who is responsible for modeling the steady state CSTR and PFR operation for the company in order to select one of them. The reactor which has smaller volume for the desired output concentration (5% of its initial value) will be chosen for economical reasons. Waste containing stream Which one F = 60 m/min do I select? Cain = 10 g/m3 Waste containing stream F = 60 m/min Cain = 10 g/m PFR Outlet stream CSTR Z=0 Z a) Draw a sketch of the PFR system with your parameters. Note that waste A decomposes into nonhazardous component B with respect to first order kinetics, ra = kCA where k = 0.09 min1. Write your assumptions. Derive a steady state ODE model of the system using a shell balance in order to describe the change of the concentration of waste A as a function of axial position z, in other words, what is CA(z)=? State the initial condition of your model. How much PFR volume is required to obtain an output A concentration of 5% of its initial value? b) Draw a sketch of the CSTR system with your parameters. Derive the steady state model of the system with an output A concentration of 5% of its initial value. Write your assumptions. Note that waste A decomposes into nonhazardous component B with respect to first order kinetics, ra = kCA where k = 0.09 min. Consider constant volume operation. What would be the CSTR volume required to obtain an output A concentration of 5% of its initial value? c) Assume that steady state PFR model you generated in part a) will be modified such that waste A decomposes into a nonhazardous component B with respect to second order kinetics, ra = KCA? where k = 0.09 min 'g 'm. What is the PFR volume required to obtain an output A concentration of 5% of its initial value at steady state? d) Assume that steady state CSTR model you generated in part b) will be modified such that waste A decomposes into a nonhazardous component B with respect to second order kinetics, ra = kCA? where k = 0.09 min 'g 'm. Considering constant volume steady state operation, what would be the CSTR volume required to obtain an output A concentration of 5% of its initial value at steady state? Based on your results in parts a), b), c), and d), fill out the following table: V PFR (m) VCSTR (m) 1st order reaction a) b) 2nd order reaction c) d)
