Continuous Stirred Tank Reactor
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Transcript of Continuous Stirred Tank Reactor
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