Question

Homework 3 Problem: A reaction A->R takes place in a constant-volume isothermal CSTR. The component mass balances are:

r= dCa/dt= Cai - Ca - KCaٍ

r= dCr/dt=Cri-Cr +KCaCr

where: CAi: feed concentration of A (input); CRi: feed concentration of R (assumed constant); CA, CR concentrations of AR, respectively, in the reactor and outlet; r,k, positive constants.

a) Linearize the equations around the design steady-state (CAis ,CA, CR) and put them in deviation variable form.

b)Calculate the transfer function between CR and CA.

c) Under what conditions on the process parameters and steady state values is the

above transfer function stable?

d) Does the above transfer function comespond to an overdamped or underdamped system? Explain

Answer 1

Now, this is a first oreder transfer function, bu the question asks to find the damping factors. Thus, I am very sure we need a second order transfer function. Thus, the question provided here must have CA by mistake and the actual question must have been to find a transfer function between C_R and C_Ai. Proceeding with that,