The dynamic response of a reactant concentration in the reactor, CA to a step

change in inlet concentration (C'A0) is to be evaluated for an isothermal, constant-

volume, constant density CSTR where only a single chemical reaction occurs. The

reaction rate is modeled by the following rate equation.

-TA

k CA

1 + koCA

(a) Derive the state equation for the system.

(b) Linearize the model in terms of deviation variables. What is the transfer

function?

(c) What are the time constant and gain for the system?

(d) Given:

kip

= 1 hour

-1

ki2

11

mimole-t

V

2 m3 F

1 mhour-1

CAO

0.5 mole m

-3

and change in CA0, i.e. ACAO

Amolem

-3

. Derive an

expression for the outlet concentration CA as a function of time t. What is

the outlet concentration after 1 hour?

(e) How does the time constant change when k1 changes from O to o? How

does it change when k2 changes from 0 to co? Do the results make sense?

Rationalize.

Question 3 (5 points) The dynamic response of a reactant concentration in the reactor, CA to a step change in inlet concentration (CA) is to be evaluated for an isothermal, constant- volume, constant density CSTR where only a single chemical reaction occurs. The reaction rate is modeled by the following rate equation. KICA -TA= 1 + KCA 2 (a) Derive the state equation for the system. (b) Linearize the model in terms of deviation variables. What is the transfer function? D (c) What are the time constant and gain for the system? (d) Given: k 1 hour 1 kg = 1 m mole-I, V = 2 m F = 1 m'hour- CA=0.5 mole m3. and change in Co. i.e. ACA = Imolem-3. Derive an expression for the outlet concentration C as a function of time t. What is the outlet concentration after 1 hour? m 9 (e) How does the time constant change when I changes from 0 to oc? How does it change when k2 changes from 0 to oo? Do the results make sense? Rationalize