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//Harriot P.,2003,Chemical Reactor Design (I-Edition) Marcel Dekker,Inc.,USA,pp 436.
//Chapter-1 Ex1.4 Pg No. 23
//Title: Activation energy from packed bed data
//=========================================================================================================
clear
clc
clf
// COMMON INPUT
L= [0 1 2 3 4 5 6 9];//Bed length in feet(ft)
T=[330 338 348 361 380 415 447 458 ] //Temperature Corresponding the bed length given (°C)
R=1.98587E-3;//Gas constant (kcal/mol K)
//CALCLATION (Ex1.4.a)
//Basis is 1mol of feed A(Furfural) X moles reacted to form Furfuran and CO
x=(T-330)./130;//Conversion based on fractional temperature rise
n=length (T);//6 moles of steam per mole of Furfural is used to decrease temperature rise in the bed
P_mol=x+7;//Total No. of moles in product stream
for i=1:(n-1)
T_avg(i)= (T(i)+T(i+1))/2
P_molavg(i)= (P_mol(i)+P_mol(i+1))/2
delta_L(i)=L(i+1)-L(i)
k_1(i)=((P_molavg(i))/delta_L(i))*log((1-x(i))/(1-x(i+1)))
u1(i)=(1/(T_avg(i)+273.15));
end
v1=(log(k_1));
i=length(u1);
X1=[u1 ones(i,1) ];
result1= X1\v1;
k_1_dash=exp(result1(2,1));
E1=(-R)*(result1(1,1));
//OUTPUT (Ex1.4.a)
//Console Output
mprintf('\n OUTPUT Ex1.4.a');
mprintf('\n========================================================================================\n')
mprintf('L \t \t T \t\t x \t\t T_average \t(7+x)ave \tk_1')
mprintf('\n(ft) \t \t (°C) \t\t \t\t (°C) \t ')
mprintf('\n========================================================================================')
for i=1:n-1
mprintf('\n%f \t %f \t %f ',L(i+1),T(i+1),x(i+1))
mprintf('\t %f \t %f \t %f',T_avg(i),P_molavg(i),k_1(i))
end
mprintf('\n\nThe activation energy from the slope =%f kcal/mol',E1 );
//=====================================================================================================
//Title: II Order Reaction
//=========================================================================================================
//CALCULATION (Ex 1.4.b)
for i=1:(n-1)
T_avg(i)= (T(i)+T(i+1))/2
P_molavg(i)= (P_mol(i)+P_mol(i+1))/2
delta_L(i)=L(i+1)-L(i)
k_2(i)=((P_molavg(i))/delta_L(i))*((x(i+1)-x(i))/((1-x(i+1))*(1-x(i))))
u2(i)=(1/(T_avg(i)+273.15));
end
v2=(log(k_2));
plot(u1.*1000,v1,'o',u2.*1000,v2,'*');
xlabel("1000/T (K^-1)");
ylabel("ln k_1 or ln k_2");
xtitle("ln k vs 1000/T ");
legend('ln k_1','ln k_2');
j=length(u2);
X2=[u2 ones(j,1) ];
result2= X2\v2;
k_2_dash=exp(result2(2,1));
E2=(-R)*(result2(1,1));
//OUTPUT (Ex 1.4.b)
mprintf('\n OUTPUT Ex1.4.b');
mprintf('\n========================================================================================\n')
mprintf('L \t \t T \t\t x \t\t T_average \t(7+x)ave \tk_2')
mprintf('\n(ft) \t \t (°C) \t\t \t\t (°C) \t ')
mprintf('\n========================================================================================')
for i=1:n-1
mprintf('\n%f \t %f \t %f ',L(i+1),T(i+1),x(i+1))
mprintf('\t %f \t %f \t %f',T_avg(i),P_molavg(i),k_2(i))
end
mprintf('\n\nThe activation energy from the slope =%f kcal/mol',E2 );
//FILE OUTPUT
fid= mopen('.\Chapter1-Ex4-Output.txt','w');
mfprintf(fid,'\n OUTPUT Ex1.4.a');
mfprintf(fid,'\n========================================================================================\n')
mfprintf(fid,'L \t \t T \t\t x \t\t T_average \t(7+x)ave \tk_1')
mfprintf(fid,'\n(ft) \t \t (°C) \t\t \t\t (°C) \t ')
mfprintf(fid,'\n========================================================================================')
for i=1:n-1
mfprintf(fid,'\n%f \t %f \t %f ',L(i+1),T(i+1),x(i+1))
mfprintf(fid,'\t %f \t %f \t %f',T_avg(i),P_molavg(i),k_1(i))
end
mfprintf(fid,'\n\nThe activation energy from the slope =%f kcal/mol',E1 );
mfprintf(fid,'\n\n========================================================================================\n')
mfprintf(fid,'\n OUTPUT Ex1.4.b');
mfprintf(fid,'\n========================================================================================\n')
mfprintf(fid,'L \t \t T \t\t x \t\t T_average \t(7+x)ave \tk_2')
mfprintf(fid,'\n(ft) \t \t (°C) \t\t \t\t (°C) \t ')
mfprintf(fid,'\n========================================================================================')
for i=1:n-1
mfprintf(fid,'\n%f \t %f \t %f ',L(i+1),T(i+1),x(i+1))
mfprintf(fid,'\t %f \t %f \t %f',T_avg(i),P_molavg(i),k_2(i))
end
mfprintf(fid,'\n\nThe activation energy from the slope =%f kcal/mol',E2 );
close;
//============================================================END OF PROGRAM===========================================
//Disclaimer (Ex1.4.a):The last value of tavg and k_1 corresponding to L=9 in Table 1.6 (Pg No. 25)of the textbook is a misprint.
// The value should be 452.5 and 4.955476 respectively instead of 455 and 18.2 as printed in the textbook.
//Hence there is a change in the activation energy obtained from the code
// The answer obtained is 21.3935 kcal/mol instead of 27 kcal/mol as reported in the textbook.
//Figure 1.8 is a plot between ln k_1 vs 1000/T instead of k_1 vs 1000/T as stated in the solution of Ex1.4.a
//=========================================================================================================
//Disclaimer (Ex1.4.b): There is a discrepancy between the computed value of activation energy and value reported in textbook
// Error could have been on similar lines as reported for example Ex.1.4.a
// Further, intermeidate values for Ex.1.4.b is not available/ reported in textbook and hence could not be compared.
//Figure 1.8 is a plot between ln k_2 vs 1000/T instead of k_2 vs 1000/T as stated in the solution of Ex1.4.b
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