Problem

The elementary liquid phase reactionis carried out in a CSTR. Pure A is fed at a rate of 2...

The elementary liquid phase reaction

is carried out in a CSTR. Pure A is fed at a rate of 200 lb mol/h at 530 °R and a concentration of 0.5 lb mol/ft3. [M. Shacham, N. Brauner, and M. B. Cutlip, Cliem. Engt: Edu. 28 (I), 30 (Winter 1994).] The mass density of the Solution is constant at 50 lbm/ft3.

(a) Plot G(T) and R(T) as a function of temperature
(b) What are the steady-state concentrations and temperatures? [One answer T = 628.645 °R, CA = 0.06843 lb mol/ft3.] Which ones are stable? What is the extinction temperature?
(c) Apply the unsteady-state mole and energy balances to this system. Consider the upper steady state. Use the values you obtained in part (b) as your initial values to plot CA and T versus time up to 6 hours and then to plot CA versus T. What did you find? Do you want to change any of your answers to part (b)?
(d) Expand your results for part (c) by varying Ta and Ta. [Hint: Try T„ = 590 °R], Describe what you find.
(e) What are the parameters in part (d) for the other steady states? Plot T and CA as a function of time using the steady-state values as the initial conditions at the lower steady state for Ta = 550 °R and Ta = 560 °R. Start at the lower steady state (T = 547.1 °R, CA = 0.425 lb mol/ft3) and make a Ca/T phase-plane plot for the base case in part (a) Ta = 530 °R. Now increase Ta to 550 °R and then to 560 °R, and describe what you find. Vary Ta.
(f) Explore this problem. Write a paragraph describing your results and what you learned from this problem.
(g) Read Section 9.3 on the CD-ROM. Carry out a linearized stability analysis. What were your values of A, B, C, τ, J, L, and M? Find the roots for the upper, lower, and middle steady states you found in part (a).
(h) Normalize x and y by the steady-state values, x1= a/CAs and y1 = y/Ts and plot .vl and yl as a function of time and also a1 as a function of yI Plot .vl and yl as a function of time for each of the three steady states. [Hint: First try initial values of, v and y of 0.02 and 2, respectively.]