The isothermal reactor in Figure 1 is used to obtain product B from reaction AB, with a reaction rate equal to _A= KC_A². The reactor has an alarm installed to control the concentration of reagent A at the outlet, which must not exceed a value of 0.35 mol/m. Assume that the reactor has good agitation, eliminating concentration profiles inside the tank. Also assume that in the process the volume remains constant. Steady state values: Fig 1. Isothermal reactor

Reservoir volume = 5 m F₁ =0.5 m/h C_A1=3.0 mol/m F₂= 0.5 m/h C_A2= 1.5 mol/m k= 5 m/mol h Determine:

a) The mathematical model in deviation variables and the initial condition for C'_A3(0).

b) The Transfer Function that relates the output C'_A3(S) and the inputs C'_A1(S) and C'_A2 (S). The process parameters Tp and Kpi numerical values and units of the parameters.

c) If the process undergoes a step disturbance with amplitude A = 2 at the input concentration C_A2(t) and at the same time there is a step disturbance with amplitude A = 2 at the input concentration C_A1(t). In this case will the alarm ring? If so, how long will it take?

d) If the process suffers a sinusoidal disturbance with amplitude A = 3 and w=1 at the input concentration C_A2(t), what will be the response in the transient state C_A3(t) and value of C_A3(t) in the new steady state? Sketch the graph for the behavior of Cas(t). What will be the value of AR?

AR = Output Amplitude / Input Amplitude

Sinusoidal input

Step entrance

U(s)=s2+w2Aw U(s)=sA