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Continuous Stirred Tank Reactor

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

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1000 lit/hr 100 lit/hr 1000 lit/hr C A0 =1 mol/lit V1CA1K1V1CA1K1 V2CA2K2V2CA2K2 V3CA3K3V3CA3K3 V4CA4K4V4CA4K4 C A1 C A2 C A3 C A4

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

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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. ReactorV i (L)K i (h -1 ) 110000.3 215000.4 31000.1 45000.2

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Solution

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Material balance continued:

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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);

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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

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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);

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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)');

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Steady state result predicted : At steady state, the concentration in tanks 1,2,3 and 4 as predicted by the programme: [C A1 C A2 C A3 C A4 ]= [0.9091 0.6969 0.6654 0.5856]

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

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