Question: The behavior of the single CSTR with the kinetics shown below is considered in this question. The goal is to control the concentration of product D in the effluent. Your supervisor proposes the feed concentration of reactant
A as the manipulated variable for a feedback controller. Is this a good idea?
In answering this question, you may use the following information:
(1) the tank is well mixed and has a constant volume and temperature;
(2) all components have the same molecular weights and densities;
(3) all reactions are elementary; thus, in this case they are all first-order;
(4) the volumetric feed flow is constant (F) and contains only component A (CAD).
(a) Starting with fundamental balances, derive the model (differential equations) that must be solved to determine the behavior of the con centration of component D.
(b) Express the equations from part id) in linearized deviation variables and define the time constants and gains.
(c) Does a causal relationship exist between CAD and CD?