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

1000 lit/hr

100 lit/hr100 lit/hr

1000 lit/hr

CA0=1 mol/lit

V1

CA1

K1

V2

CA2

K2

V3

CA3

K3

V4

CA4

K4

CA1 CA2 CA3 CA4

• 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

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 constantsCA0=1;V1=1000; K1=0.1; %data from tableV2=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 resultsfunction 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 theplot depicting the variation of Concentration ineach tank:

clcclear allx0=[1;0;0;0]; %defining the initial values.[t,x]=ode45(@fourcstr, [0 0.1], x0); %ode45 to solve the

unsteady statefigure;plot(t,x); %plot function%labelling x and y axesxlabel('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