Problem 1 This is an extension of the CSTR with second order kinetics example solved in class. Considering the system of two CSTRS as shown in the schematic below, determine

the dynamic behavior of the reactor concentrations (CA1 and CÃ2) in response to a step change in inlet concentration, CÃO. Estimate the time it takes until 95% of the change in outlet concentration of reactor 2 has occurred. Data ● e. ● ● Fo=F₁ F₂ = 0.25 m³/min V₁=5 m³ V₂ = 4 m³ Initially,CAO =1.5 mole/ m³ TAI -K * CAI 0.5 for i= 1, 2 K = 0.05 (min*(mole/m3)0.5)-¹ ACAO 1.0 mole/ m³ (step change in inlet concentration) at time t=5 min (time of step change should be variable in your Excel program) The system is initially at steady state, flowrates remain constant, perfect mixing in tanks. = Specifically, a. Summarize your data b. State any assumptions you make. C. Derive the non-linear model for the dynamic response of the concentration of A in the reactor, CÂ(t). Show all your derivations/calculations. d. Use the Euler method to solve the non-linear model for a step change in the inlet concentration, CAO, of size +1 mole/m³. Plot the non-linear responses of the system, i.e. make a plot of CAO, CA1 and CA2 .vs. time Fo ENGR 4306 HW 2 3 CAD V₁, CA1 ₁₁=-K.C₁ 0.5 F₁ V₂, CA2 F₂ 42 = -K.C ₁2 0.5 A2 Problem 2 Consider the isothermal and well-mixed chemical reactor shown in the schematic below. The rate of reaction occurring in the reactor is: r = -k Có. Initially, the system is at steady state conditions and the flow rate in and out from the reactor, F, is 0.2m³/min. Also, the initial inlet concentration of component A, CAOS, is 2 mole/m³ and the reactor volume, V, is 5 m³. The reaction constant, k, is 0.5 (mole / m³)-² * min¹. If the density change due to the reaction is zero and the flow rates in and out from the reactor remain constant, then: a) Summarize your data b) State any assumptions you make. c) Derive the non-linear model for the dynamic response of the concentration of A in the reactor, CÂ(t). Show all your derivations/calculations. d) Use the Euler method to solve the non-linear model for a step change in the inlet concentration, CAO, of size +1 mole/m³. e) Plot the non-linear responses of the system, i.e. make a plot of CAO and CA .vs. time F CAD AO C, A V r₁ = -K.C₂₁³ 3 Notes: 1. Follow the HW structure/rubric to prepare solution to above problems. 2. Your simulation results and numerical solutions must be in Excel (to support your report). 3. Make sure you follow the Model Development Methodology. 4. Show all your calculations