Additional Homework Problems

		A heat exchanger and a controller are to be added to the ammonium nitrate reactor discussed in Problem P9-3 from the 4th edition of Elements of Chemical Reaction Engineering. The reactor temperature is to be controlled by manipulating the coolant flow rate, in the heat exchanger. The ambient temperature at the time the controller is turned on is 970°R. The product of the heat-transfer coefficient and heat-exchanger area is UA = 10,000 Btu/h°F.

		The controller is to be a PI controller with an integral time, of 1 h and a gain of -4.5°. A sudden upset causes the reactor temperature to rise to 1000°R, which is 25°R above the set point.

		For each of the following three cases, plot the reactor temperature and mass in the reactor, M, as a function of time. [Hint: First show that the energy balance can be written as



		(a) Consider Mconstant at 300 lb. (b) Calculate M from a mass balance, that is,



		The set-point of the mass in the tank is 325 lb. (c) Consider no control by setting the controller gain equal to zero (i.e., k_C = 0.) (d)Vary k_Cand describe what you find. (e) Vary UA,_C ,, and so on, and describe what you find.