A closed stirred-tank reactor with two compartments is shown in figure. The basic idea is to feed the reactants continuously into the first compartment where they will be preheated by energy Liberated in the exothermic reaction, which is anticipated to occur primarily in the second compartment. The wall separating the two compartments is quite thin, thus allowing heat transfer; the outside of the reactor is well insulated; and a cooling coil is built into the second compartment to remove excess energy liberated in the reaction. Tests are to be conducted initially with a single-component feed (i.e., no reaction) to evaluate the reactor’s thermal characteristics.

(a) Develop a dynamic model for this process under the conditions of no reaction. Assume that q, T_i, and T_c all may vary.

(b) Make a degrees of freedom analysis for your model—identifying all parameters, outputs, and inputs that must be known functions of time in order to obtain a solution.

(c) In order to estimate the heat transfer coefficients, the reactor will be tested with Ti much hotter than the exit temperature. Explain how your model would have to be modified to account for the presence of the exothermic reaction. (For purposes of this answer, assume the reaction is A - B and be as specific as possible.)

Notes:

U₁, A_i: Overall heat transfer coefficient and surface area between compartments.

U_c, A_c Overall heat transfer coefficient and surface area of cooling tube.

V₁: Volume of Compartment 1.

V₂: Volume of Compartment 2.

Coling medium T. 92 T2 40 V2 T2 T TL V1