1. An autocatalytic chemical reaction is being undertaken in an isothermal CSTR. In this reaction, species A is being converted into species B but there is also an amount of (unwanted) degradation of B into C. A +2B ki, 3B B k2C = = = Writing a state vector in terms of the concentration of the species involved, x = [CA, CB]T, the system can be modelled by the following set of (dimensionless) differential equations: dx [F(21i 21) - 1123) dt -(K+F).22 +2133 where F = kiv 0.50 (the reciprocal of the Damkhler number), Ili is the incoming feed concentration of species A (there is no feed of species B) and k = k2/k = 0.10. The reactor has been operating with Ili = 1.90. (a) What are the steady states? Identify their stability and give a physical interpretation of each steady state. (b) By plotting trajectories, draw a phase portrait for the model in these conditions over a region of interest I1 (0,2.5), 12 (0,2.5) (hint: draw trajectories starting on the left and right sides of the figure). (c) Species B is a potentially explosive compound and plant operations must ensure that the concentration never exceeds CB = 1.6. By qualitative analysis of the features of the phase portrait, what can you conclude about suitable initial conditions for starting the reaction? Indicate on the phase portrait what region of initial conditions would be acceptable (shading the region by hand on the plot is fine, drawing in some lines and labelling electronically is fine too; please don't edit your PDF in any PDF annotation software). (d) The plant operations manager has proposed to reduce the inlet concentration to the reactor to Ili = 1.50. Draw a phase portrait for these new conditions over the same region of interest. Is the manager's proposal acceptable? Justify your conclusions. 1. An autocatalytic chemical reaction is being undertaken in an isothermal CSTR. In this reaction, species A is being converted into species B but there is also an amount of (unwanted) degradation of B into C. A +2B ki, 3B B k2C = = = Writing a state vector in terms of the concentration of the species involved, x = [CA, CB]T, the system can be modelled by the following set of (dimensionless) differential equations: dx [F(21i 21) - 1123) dt -(K+F).22 +2133 where F = kiv 0.50 (the reciprocal of the Damkhler number), Ili is the incoming feed concentration of species A (there is no feed of species B) and k = k2/k = 0.10. The reactor has been operating with Ili = 1.90. (a) What are the steady states? Identify their stability and give a physical interpretation of each steady state. (b) By plotting trajectories, draw a phase portrait for the model in these conditions over a region of interest I1 (0,2.5), 12 (0,2.5) (hint: draw trajectories starting on the left and right sides of the figure). (c) Species B is a potentially explosive compound and plant operations must ensure that the concentration never exceeds CB = 1.6. By qualitative analysis of the features of the phase portrait, what can you conclude about suitable initial conditions for starting the reaction? Indicate on the phase portrait what region of initial conditions would be acceptable (shading the region by hand on the plot is fine, drawing in some lines and labelling electronically is fine too; please don't edit your PDF in any PDF annotation software). (d) The plant operations manager has proposed to reduce the inlet concentration to the reactor to Ili = 1.50. Draw a phase portrait for these new conditions over the same region of interest. Is the manager's proposal acceptable? Justify your conclusions
