Review the example problems in this chapter, choose one, and use a software package such a...

Review the example problems in this chapter, choose one, and use a software package such as Polymath or MATLAB to carry out a parameter sensitivity analysis.

What if…

(a) Example 9–1. How much time would it take to achieve 90% conversion if the reaction were started on a very cold day where the initial temperature was 20 °F? (Methanol won’t freeze at this temperature.)

(b) Example 9–2. Explore the ONCB explosion described in Example 9–2. Show that no explosion would have occurred if the cooling was not shut off for the 9.04-kmol charge of ONCB or if the cooling was shut off for 10 min after 45 min of operation for the 3.17-kmol ONCB charge. Show that if the cooling had been shut off for 10 min after 12 h of operation, no explosion would have occurred for the 9.04-kmol charge. Develop a set of guidelines as to when the reaction should be quenched should the cooling fail. Perhaps safe operation could be discussed using a plot of the time after the reaction began at which the cooling failed, t0, versus the length of the cooling failure period, tf, for the different charges of ONCB. Parameter values used in this example predict that the reactor will explode at midnight. What parameter values would predict the time the reactor would explode at the actual time of 18 min after midnight? Find a set of parameter values that would cause the explosion to occur at exactly 12:18 a.m. For example, include heat capacities of metal reactor and/or make a new estimate of UA. Finally, what if a 1/2-in. rupture disk rated at 800 psi had been installed and did indeed rupture at 800 psi (270 °C)? Would the explosion still have occurred? (Note: The mass flow rate hi varies with the cross-sectional area of the disk. Consequently, for the conditions of the reaction the maximum mass flow rate out of the 1/2-in. disk can be found by comparing it with the mass flow rate of 830 kg/min of the 2-in. disk.

(c) Example 9–3. What would be the conversion at the onset temperature if the heating rate were reduced by a factor of 10? Increased by a factor of 10?

(d) Example 9–4. What would the X versus t and T versus t trajectories look like if the coolant rate is decreased by a factor of 10? Increased by a factor of 10?

(e) Example 9–5. Load the Living Example Problem for Startup of a CSTR for an entering temperature of 70 °F, an initial reactor temperature of 160 °F, and an initial concentration of propylene oxide of 0.1 M. Try other combinations of Ti, Th and CAi, and report your results in terms of tern- perature-time trajectories and temperature-concentration phase planes.

(f) Example 9–6. Load the Living Example Problem for Falling Off the Upper Steady State. Try varying the entering temperature, T0, between 80 and 68 °F and plot the steady-state conversion as a function of T0. Vary the coolant rate between 10,000 and 400 mol/h. Plot conversion and reactor temperature as a function of coolant rate.

(g) Example 9–7. What happens if you increase the heat transfer coefficient by a factor of 10 and decrease Ta to 280 K? Which trajectories change the most?

(h) Example RE9-1. Load the Living Example Problem. Vary the gain, kc between 0.1 and 500 for the integral controller of the CSTR. Is there a lower value of kc that will cause the reactor to fall to the lower steady state or an upper value to cause it to become unstable? What would happen if T0 were to fall to 65 °F or 60 °F?

(j) Example RE9-2. Load the Living Example Problem. Learn the effects of the parameters kc and x,. Which combination of parameter values generates the least and greatest oscillations in temperature? Which values of kc and x, return the reaction to steady state the quickest?

(j) Reactor Safety. Enter the SACHE web site, www.sache.org. [Note you will need to obtain the user name and password for your school from your department chair or SACHE representative.] After entering hit the current year (e.g., 2004). Go to product: Safety, Health and the Environment (S,H,&E). The problems are for KINETICS (i.e., CRE). There are some example problems marked K and explanations in each of the above S,H,&E selections. Solutions to the problems are in a different section of the site. Specifically look at: Loss of Cooling Water (K-l) Runaway Reactions (HT-1), Design of Relief Values (D-2), Temperature Control and Runaway (K-4) and (K-5), and Runaway and the Critical Temperature Region (K-7).