Post on 08-Apr-2018
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Assignment 01
Process Modeling and
Simulation
Name:K.S.M.S.Senarath
Index No: 050418H
Date of Sub: 02.02.2009
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01.Pendulum ProblemMomentum equation of a pendulum is given as below when initial faorce of
the pendulum is zero.
In Matlab code I took angle as y(1) and angular velocity as y(2).
Code in Pendulum M-File
function dydt=pendulum(t,y)g=9.81; % Gravitational Accelaration (ms-2)
M=3; % Mass of the rod (kg)
I=12; % Inertia (kgm2)
R=sqrt(2*I/M); % Radius (m)
f1=y(2);
f2=-M*g*R*sin(y(1))/I
dydt=[f1;f2];
Code in Command Window
>> y0=[pi/3,0];
>> tspan=[0,10];
>> [t,y]=ode45(@pendulum,tspan,y0);
>> plot(t,y)
>> xlabel('Time\it (S)')
>> grid
>>legend('\it Angular Acceleration','\it Angular
Velocity')
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Obtained Graph for Angular acceleration and angular Velocity
0 1 2 3 4 5 6 7 8 9 10-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Time (S)
Angular Accelaration
Angular Velocity
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02.Temperature Variation in Plates of Binary Distillation TowerThis binary distillation tower distills Benzene and Toluene. Below equation
will be used for construct the MatLab model.
For the total mass balance of the system
F = W + D
Composition Mass Balance
F.XF= W.XW + D.XD
Equation of Top Operating Line
Equation of q Line
Where
F Feed Rate (kmol/hr)
X- Liquid composition of Benzene
Y- Gas Composition of Benzene
D Distilled product (kmol/hr)
D, XD
V, XD
F, XF
Lo
W, XW
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W - Bottom Product (kmol/hr)
In M-File
%-------------K.S.M.S.Senarath----------------%
%--------------------------050418H----------------------%
clear all
%--Liquid & Gas composition data for Benzene & Toluene--%
X= [0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800
0.900 0.950 1.000];
%Composition of liquid (Benzene)
Y= [0.000 0.208 0.372 0.507 0.612 0.713 0.791 0.857 0.912
0.959 0.980 1.000];
%Composition of gas (Benzene)
T= [110 105.3 101.5 98.0 95.1 92.3 89.7 87.3 85.0 82.7
81.4 80.1];
%Boiling points of mixtures
%--------Data of Distillation Tower----------%
F=120; %Feed rate (kmol/hr)
D=23.75; %Product Rate (kmol/hr)
Xf=0.45; %Feed composition
Xd=0.98; %Distillate composition
P=1; % Operating pressure (atm)
R=1.5; %Reflux Ratio
%---------Calculate W, Xw and coefficients of BOL--------%
W=F-D; %Bottom Flow Rate (kmol/hr)
Xw=(F*Xf-D*Xd)/W; %Bottom Composition
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Yf=R*Xf/(R+1)+Xd/(R+1); %Point of Intersection of TOL &
BOL
m=(Yf -Xw)/(Xf -Xw); %Gradient
c=Xw-m*Xw; %Intersection
fprintf ('Bottom Flow rate: %.2f kmol/hr \n',W)fprintf ('Bottom Composition: %.2f \n',Xw)
%----------Polynomials of Equilibrium Curves-----------%
A= polyfit(X,Y,5);
%Coefficients of the Polynomial (Y vs X)
B= polyfit(X,T,5);
%Coefficients of the Polynomial (Temperaturevs. X)
comp_temp=zeros(50,2);
%-----Composition Calculation of Partial Condenser)-----%
Z=zeros(1,6);
Z=A;
Z(6)=A(6)-Xd;
r=roots(Z);
for i=1:5
if (r(i,1)0)&(imag(r(i,1))==0)
x=r(i,1);
comp_temp (1,1)=x;
end
end
%--------------Plate Calculation-------------%
for i=1:49
x=comp_temp(i,1);
y=R*x/(R+1) + Xd/(R+1);
%Top Operating Line Equation
Z(6)=A(6)-y;
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a=roots(Z);
for j=1:5
if (a(j,1)0)&(imag(a(j,1))==0)
%Find the Correct between 0 & 1
x=a(j,1);if x>=Xf
%check the condition for feed composition
comp_temp(i+1,1)=x;
else
y=m*x + c;
%bottom operating line
Z(6)=A(6)-y;
a=roots (Z);
for k=1:5
if
(a(k,1)0)&(imag(a(k,1))==0)
%Correct Root
x=a(k,1);
if Xw 0
comp(k,1)=comp_temp(k,1);
else
break
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end
end
N=length(comp);
NN=1:1:N;T=polyval(B,comp);
subplot(2,1,1),plot(NN,comp,'r')
grid on
xlabel ('Plate No.(From Top)')
ylabel ('Liquid Composition-Benzene')
subplot (2,1,2),plot(NN,T,'b')
grid onxlabel ('Plate No:(From Top)')
ylabel ('Plate Temperature(0C)')
fprintf ('No of plates: %.0f \n',N-2)
Comp_Temp= [Composition T]
return
end
end
end
end
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Results
In Command Window
>> Bottom Flow rate: 96.25 kmol/hr
Bottom Composition: 0.32
No of plates: 12
Temperature Variation in plates of distillation tower