1. Continuous Stirred Tank Reactor

2. Problem statement
A chemical reaction takes place in a series of four continuous stirred tank reactors arranged as shown in Fig

3. 100 lit/hr 100 lit/hr 1000 lit/hr CA0=1 mol/lit 1000 lit/hr CA1 CA2V1
CA 1 K1 V2
CA 2 K2 V3
CA 3 K3 V4
CA 4 K4
1000 lit/hr
CA1
CA2
CA3
CA4

4. The chemical reaction is a first order irreversible reaction of the type-
A B
The value of the rate constant ki, is different in each reactor. Also, the volume of each reactor Vi is different k

5. Assumptions: The system is steady state and unsteady state.
The reactions are in liquid phase.
There is no change in volume or density of the liquid.
Reactor
Vi(L)
Ki(h-1) 1
1000
0.3 2
1500
0.4 3
100
0.1 4
500
0.2

6. Solution

7. Material balance continued:

8. Using MATLAB for steady state results
function f=fourcstrsteady(x)
f=zeros(4,1);
%defining constants
CA0=1;
V1=1000; K1=0.1; %data from table
V2=1500; K2=0.2;
V3=100; K3=0.4;
V4=500; K4=0.3;
xa=x(1);xb=x(2);xc=x(3);xd=x(4);
%material balance equations:
f(1)=(1000*CA0)-(1000*xa)-(V1*K1*xa);
f(2)=(1000*xa)+(100*xc)-(1100*xb)-(V2*K2*xb);
f(3)=(1100*xb)+(100*xd)-(1200*xc)-(V3*K3*xc);
f(4)=(1100*xc)-(1100*xd)-(V4*K4*xd);

9. Running the following displays the steady state concentrations in the tanks:
clc
clear all
x0=[0,0,0,0]; %initial values
x0) %fsolve to solve the steadystate

10. MATLAB for unsteady state results
function f=fourcstr(t,x) f=zeros(4,1); %defining constants CA0=1; V1=1000; K1=0.1;%data from the table given V2=1500; K2=0.2;%data from the table given V3=100; K3=0.4;%data from the table given V4=500; K4=0.3;%data from the table given xa=x(1);xb=x(2);xc=x(3);xd=x(4); %defining the differential equations %material balance equations assuming unsteady state f(1)=(1000*CA0)-(1000*xa)-(V1*K1*xa); f(2)=(1000*xa)+(100*xc)-(1100*xb)-(V2*K2*xb); f(3)=(1100*xb)+(100*xd)-(1200*xc)-(V3*K3*xc); f(4)=(1100*xc)-(1100*xd)-(V4*K4*xd);

11. Running the following code in MATLAB yields the
plot depicting the variation of Concentration in
each tank:
clc
clear all
x0=[1;0;0;0]; %defining the initial values.
[0 0.1], x0); %ode45 to solve the unsteady state
figure;
plot(t,x); %plot function
%labelling x and y axes
xlabel('time t(hrs)');
ylabel('concentration c(t)');

12. Steady state result predicted :
At steady state, the concentration in tanks 1,2,3 and 4 as predicted by the programme: [CA1 CA2 CA3 CA4]= [ ]

13. Unsteady state results
The following variation is predicted with respected to time