Consider the chemical reactor/separator systems shown below, one with a recycle stream and one without a recycle stream. Without Recycle Fo, Xi (A and C only) Fs, XS Fo, Xi (A

and C only) F1, X1 With Recycle F1, X1 CSTR A→B Fs, X3 CSTR A→B (A and C only) F1, X2 F3, X3 (A and C only) F1, X2 F3, X3 SEPARATOR SEPARATOR (B only) F6, X3 (B only)/nFO= 1.0 F1 2.7 F3 = 1.8 F5 = 1.7 Xi A0 = 0.95 T = 1/2.7 KO = 2.7 #moles/time # moles/time # moles/time # moles/time # moles fraction #time # 1/time X1_A0 = 2/3 #moles fraction X2_A0 1/3 #moles fraction X3_A0 1/2 #moles fraction X5_A0 = 1/2 #moles fraction Assumptions Constant molar hold-up for CSTR. All molar flowrates are constant. Perfect separation unit with infinitely fast dynamics. • No transportation delay between separator and fast dynamics. • Isothermal process. Mixing Point Subsystem F₁ = F₁+F₂ F₁x₁₁A= Fox₁.A + F5X3,A (1)/nReactor Subsystem d(MX2,A) = F₁X₁,A - F₁X2₂‚A¬K₁X2,AM dt or dx2,A 1 dt -=-—- (X1₁,4 – X2,A) — K₁X2,A (2) M F₁ Separator Subsystem F₁X2,4 = F3X3,A (3)/nWithout Recycle Case X'iA X'S,A G4 G3 X'LA G₁ X'3,A G₂ X'2A 1. Develop the transfer function in the block diagram representation of the system without recycle. In this block diagram, the variables are deviation variables (for example, x'i,A = xi,A-xi,A_steady_state). 2. Using Python, simulate the dynamic system by using a step change in xi,A from 0.95 to 0.96 at t=2. Plot the response results of each variable in this order xi,A, x1,A, x2,A, x3,A, in a 4-by-1 subplot. 3. Using Python, fit a transfer function to the step response of x3,A and compare the key parameters with the theoretical parameters obtained in step-1.