The exercise involves creating a dynamic model based on balance equations, linearizing, and putting the equations into state space form. This is a highly nonlinear process that is prone to exponential run-away when the temperature rises too quickly. By staying below the runaway temperature, the reactor stays within equipment temperature and pressure limits.
A reactor is used to convert a hazardous chemical A to an acceptable chemical B in waste stream before entering a nearby lake. This particular reactor is dynamically modeled as a Continuously Stirred Tank Reactor (CSTR) with a simplified kinetic mechanism that describes the conversion of reactant A to product B with an irreversible and exothermic reaction. Because the analyzer for product B is not fast enough for real-time control, it is desired to maintain the temperature at a constant set point that maximizes the consumption of A (highest possible temperature).
Linearize mass, species, and energy balance that describe the dynamic response in volume, concentration, and temperature of a well-mixed vessel derived as an earlier exercise on balance equations. Put the resulting model into state space form.
The inlet flow (qf= 5.0 L/min) and outlet (q = 5.0 L/min) volumetric flowrates, feed concentration (Caf = 0 mol/L), and inlet temperature (Tf=300 K) can be adjusted. Initial conditions for the vessel are V= 1.0 L, Ca = 0.0 mol/L, and T=300 K. Compare linearized and nonlinear model responses with step changes in qf to 5.2 L/min, Caf to 1 mol/L, and Tf to 325 K.