7.7 Consider an isothermal, constant-volume CSTR in which the following series-parallel reactions take place R P...

 

Transcribed Image Text:

7.7 Consider an isothermal, constant-volume CSTR in which the following series-parallel reactions take place R P B 2 R B where R is the reactant, P is the product and B, B2 are undesirable byproducts. The re- actions RP and P B have first-order kinetics, whereas 2R B2 has second-order kinetics. Component mass balances for species R and P give the following state-space model for the reactor: VdCR = F(CR-CR)-VKCR-VKC dt V dCp = -FCp+Vk,CR-VKCp dt P The reactor has two input variables: (1) the reactant concentration in the feed u = CR, in (2) the feed flowrate u = F and one output variable: the concentration of the product P in the reactor y = Cp. The following parameter values are given for the system: V = 1 L, k = 50 min-, k = 54 min, k3 = 4 min L/mol R, (a) Calculate the reactor steady state when CR in = 5.5 mol/L and F = 21 L/min. (b) Linearize the system equations around the steady state of part (a). Check if it is locally asymptotically stable. (c) Suppose that the reactor is initially at the steady state of part (a). Suddenly, at t = 0, the flowrate F increases to 28 L/min, while the feed concentration CR.in remains unchanged. Use MATLAB to simulate the output response for both the nonlinear and linearized systems, and plot the responses on a common graph. 7.7 Consider an isothermal, constant-volume CSTR in which the following series-parallel reactions take place R P B 2 R B where R is the reactant, P is the product and B, B2 are undesirable byproducts. The re- actions RP and P B have first-order kinetics, whereas 2R B2 has second-order kinetics. Component mass balances for species R and P give the following state-space model for the reactor: VdCR = F(CR-CR)-VKCR-VKC dt V dCp = -FCp+Vk,CR-VKCp dt P The reactor has two input variables: (1) the reactant concentration in the feed u = CR, in (2) the feed flowrate u = F and one output variable: the concentration of the product P in the reactor y = Cp. The following parameter values are given for the system: V = 1 L, k = 50 min-, k = 54 min, k3 = 4 min L/mol R, (a) Calculate the reactor steady state when CR in = 5.5 mol/L and F = 21 L/min. (b) Linearize the system equations around the steady state of part (a). Check if it is locally asymptotically stable. (c) Suppose that the reactor is initially at the steady state of part (a). Suddenly, at t = 0, the flowrate F increases to 28 L/min, while the feed concentration CR.in remains unchanged. Use MATLAB to simulate the output response for both the nonlinear and linearized systems, and plot the responses on a common graph.