Question: The well-mixed, constant-volume chemical reactor with separator and re cycle in Figure is considered in this question. The reactor has a single reaction A → B with r_A = -kC_A. The separator makes a perfect separation of the product and the pure reactant, which is recycled to the reactor feed, and the separator dynamics and transportation delays are very fast and will be assumed at quasi-steady state.

a) Assume that the fresh feed rate (Fi) is controlled constant. The major disturbance is temperature, which can be taken to be a change in the reaction rate constant. Based on a dynamic model of the process, determine an analytical relationship between the disturbance and

(1) the recycle flow and

(2) the reactor concentration. Determine how the dynamic behavior is affected by the steady-state conversion, (C_A0 - C_A)/C_A0

(b) Discuss the factors that would influence the choice of the best reactor conversion in a typical industrial process.

(c) Determine a simple change to the control design that substantially reduces the effect of the disturbance (without controlling temperature)