Continuous Stirred Tank Reactor
Problem statement
A chemical reaction takes place in a series
of four continuous stirred tank reactors
arranged as shown in Fig
100 lit/hr
100 lit/hr
1000 lit/hr
CA0=1
mol/lit
V1
V2
V3
V4
CA
CA
CA
CA
1
2
3
4
K1
K2
K3
K4
CA1
CA2
CA3
1000
lit/hr
CA4
• The chemical reaction is a first order
irreversible reaction of the typeA k
B
• The value of the rate constant ki, is
different in each reactor. Also, the volume
of each reactor Vi is different
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
Solution
Material balance continued:
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);
• Running the following displays the steady
state concentrations in the tanks:
clc
clear all
x0=[0,0,0,0]; %initial values
x=fsolve(@fourcstrsteady, x0) %fsolve to solve
the steadystate
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);
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.
[t,x]=ode45(@fourcstr, [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)');
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]= [0.9091 0.6969
0.6654 0.5856]
Unsteady state results
The following variation is predicted
with respected to time