Credit where it is due, this problem was taken from Scott Fogler's Elements of Chemical Reaction Engineering. I modified it to reinforce concepts from class. Consider the hydration of propylene oxide (A) using water (B) to produce propylene glycol (C). A+BC The reaction may be considered irreversible. Further, under the conditions here, water is in considerable excess so the reaction is pseudo-first order in propylene oxide. r=kCA You carry out the reaction in a 500 gallon CSTR that is equipped with a heat exchanger. Initially, the tank is filled with water at a concentration of 3.45lbmolft3 at a temperature of 75F. The feed stream consists of propylene oxide (80lbmolh1), water (1000lbmolh1), and methanol (100lbmolh1); the combined feed stream enters the reactor at a temperature of 75F. Because the feed stream is mostly water, you may assume that its density is constant as a function of both time and fractional conversion of A; i.e., the inlet volumetric flowrate is equal to the outlet volumetric flowrate. You may also assume that the volume the liquid in the tank is constant at 500 gallons. The cooling water enters the heat exchanger at 60F, and you may assume that the cooling water flowrate is sufficiently high to keep the cooling water temperature constant. You additionally have the following data available: VB=0.290ft3lbmol1VM=0.649ft3lbmol1UA=16,000BTU1R1 The rate constant for this reaction can be computed in units of h1 using the following equation where the barrier has units of B TU lb-mole 1. k=16.961012exp(RT32,400) How many steady states are possible in this system? Part 2 Compare rates of heat generation and heat removal as a function of Temperature to characterize the stability of each steady state that you identify. Create a Taylor series expansion about the steady state solution in order to linearize the (transient) material and energy balances that describe this system. Find the eigenvalues associated with each steady state solution and determine whether perturbations in temperature and/or concentration at each steady state will: 1. grow with time 2. decay with time (asympotic stability) 3. show oscillatory behavior Please note: If you assume that CP is zero for this reaction and that the heat of reaction is constant despite changes in temperature, you can reduce this to 2x2 linear system and make your life a bit easier. If you account for varying heat of reaction, it will be a 44 system. I've solved it both ways and have obtained the same results in each case, but the 22 is substantially easier. For the case where the reactor is initially filled with water and held at a temperature of 75F, simulate the reactor startup period to determine 1. how long it takes for the reactor to reach steady state 2. the fractional conversion of A and reactor Temperature at steady state. Simulate the case where the reactor is allowed to reach steady state and operate at steady state for 10 hours. At that time, the heat transfer coefficient is reduced in half due to a problem in the cooling line. This persists for 30 minutes, and then the original working capacity is restored. Plot the concentrations of each species, the fractional conversion, and the temperature in the reactor as a function of time (at least until the system reaches a second steady state)