TABLE OF CONTENTS If the differential equations for a material or energy balance are set up in the following form, the process gain (K p) and time constant ( ? p) terms, and the relative effects of process design and operating conditions, can be identified for an input X i, which is a manipulated or disturbance variable, and an output (Y), which is the process variable.
For a negative-feedback or self-regulating process, the differential equation is: [2.1]
For a positive feedback or runaway process, the differential equation is: [2.1]
If there is no process feedback, we have an integrator gain K i. [2.1]
The general equation for energy or material balance with generation and consumption terms for a reaction is:
To illustrate the methodology, the differential equations will be set up and converted to the proper form for a reactor and its coolant system. The rate of accumulation of energy in a reactor is the sensible heat of the flow in minus the flow out of the reactor plus the heat of reaction and minus the heat loss to the jacket [2.1] [2.20].
If we combine terms, we can isolate the coefficient of the process feedback.
If we divide through by the coefficient of T r we get the process time constant and gain for reactor temperature control.
If dQ r/dT r < F o*C r + U*A, and dQ r /dT r > F
