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 # moles/time Xi_A0 = 0.95 # moles fraction T = 1/2.7 #time k0 = 2.7 # 1/time X1 A0 = 2/3 X2 A0 = 1/3 X3 A0 = 1/2 X5_A0 = 1/2 Assumptions • • Mixing Point Subsystem F₁ = F₁+F₂ F₁x₁₁A=F₁x₁₁A+F5X3,A d(Mx2,4) dt or # moles/time #moles/time #moles/time 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. Reactor Subsystem dx 2.4 dt T= #moles fraction #moles fraction #moles fraction #moles fraction M = F₁X₁,4-F₁X₂₁4-kox2, AM = - - - (X₁.A - X₂,₁A) - K₁X2₂,A (2) T (1) Separator Subsystem F1X2,4 =F3X3,A (3)/nWith Recycle Case X'iA G4 G3 X'LA X'JA G₁ G₂ X'2A 4. Similarly, develop the transfer function in the block diagram representation of the system with recycle. In this block diagram, the variables are deviation variables (for example, x'i,A = xi,A - xi,A_steady_state). 5. 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 results in the same plot produced in step-2 using different line types (or colors) representing each of the two cases and include a legend. 6. 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-4. Analysis 7. By examining the results from part 5 and based on your chemical engineering knowledge, explain the behavior observed in the plot for the two cases and state any differences observed in their behavior. 8. Derive the overall transfer function from x'i,A(s) to x'3,A(s) for the two cases. How do the overall transfer functions differ? Are these results consistent with your answer for part 7?