## State Space Stirred Reactor

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 (*q _{f}= 5.0 L/min*) and outlet (

*q = 5.0 L/min*) volumetric flowrates, feed concentration (

*Ca*), and inlet temperature (

_{f}= 0 mol/L*T*) can be adjusted. Initial conditions for the vessel are

_{f}=300 K*V*= 1.0 L, Ca = 0.0 mol/L, and T=300 K. Compare linearized and nonlinear model responses with step changes in

*q*to

_{f}*5.2 L/min*,

*Ca*1 mol/L

_{f}to*, and*T

_{f}to

*325 K*.