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+
+Heat Capacity evaluated at 800 K :827 (cal/°C)
+Temperature Change to carry out the reaction at T_F,
+using the energy to heat the product gas :210 °C
+ OUTPUT Ex3.7.a
+============================================================================
+ X Phi T_eq T_eq r_max
+ - (atm^-0.5) (K) (°C) (gmol/g cat sec)
+============================================================================
+ 0.50 3636568.30 962 689 7.749486E-05
+ 0.60 736637.41 927 654 5.880675E-05
+ 0.70 171613.48 892 619 4.352732E-05
+ 0.80 31644.93 853 580 3.044561E-05
+ 0.90 12422.07 802 529 1.840952E-05
+ 0.95 7367.71 760 487 1.201510E-05
+
+
+ OUTPUT Ex3.7.b
+============================================================================
+===========================================
+ 10^-6/r X (conversion)
+ (gmol/g cat,s) (-)
+===========================================
+ 0.04 0.10
+ 0.03 0.20
+ 0.02 0.30
+ 0.01 0.40
+ 0.01 0.50
+ 0.02 0.60
+From graphical procedure (1/r vs x) the optimum temperature obtained is T_opt: 412°C \ No newline at end of file
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+//Harriot P,2003,Chemical Reactor Design (I-Edition) Marcel Dekker,Inc. USA,pp 436
+//Chapter-3 Ex3.7 Pg No. 115
+//Title:Equilibrium temperature as a function of conversion and Optimum Feed Temperature
+//==========================================================================================================
+clear
+clc
+// COMMON INPUT
+P_opt=1.5; //(atm) Operating pressure of first converter
+x=[0.5 0.6 0.7 0.8 0.9 0.95];// Conversion of SO2
+k=[2E-06 5.1E-06 10.3E-06 18E-06 27E-06 37.5E-06 48E-06 59E-06 69E-06 77E-06] ; //Rate Constant (gmol/g cat sec atm)
+T=420:20:600;// Temperature (°C)
+X=0.68;
+T_F=700;//Feed Temperature(K)
+C_pi_800=[12.53 18.61 8.06 7.51];
+F=100;// (mol) amount of feed
+delta_H_700=-23270;//(cal/mol)
+percent_SO2_f=11;//(%)Percentage of SO2 in feed
+
+
+//CALCULATION (Ex3.7.a)
+n=length(x);
+m=length(k);
+for i=1:n
+ K_eq(i)=((x(i)/(1-x(i))))*((100-5.5*x(i))/(10-5.5*x(i)))^0.5*(1/P_opt)^0.5;
+ T_eq(i)=(11412/(log(K_eq(i))+10.771));
+ P_O2(i)=(10*(10-5.5*x(i))*P_opt)/(100-5.5*x(i));
+ P_SO3(i)=(11*x(i)*P_opt)/(100-5.5*x(i));
+ P_SO2(i)=(11*(1-x(i))*P_opt)/(100-5.5*x(i));
+end
+
+for i=1:n
+ for j=1:m
+ r(j,i)=k(j)*(P_SO2(i)/P_SO3(i))^0.5*(P_O2(i)-(P_SO3(i)/(P_SO2(i)*K_eq(i)))^2)
+ end
+ r_max(i)=max(r(j,i));
+end
+clf()
+scf(0)
+plot(x,T_eq-273,'*');
+xtitle('Temperature in Stage 1 of an SO2 converter');
+xlabel('x,SO2 Conversion');
+ylabel('Temperature,°C' );
+
+//CALCULATION (Ex3.7.b)
+n_SO2=F*percent_SO2_f*10^-2*(1-X);
+n_SO3=F*percent_SO2_f*10^-2*X;
+n_O2=(10-5.5*X);
+n_N2=79;
+sigma_n_C_pi=n_SO2*C_pi_800(1)+n_SO3*C_pi_800(2)+n_O2*C_pi_800(3)+n_N2*C_pi_800(4);
+Temp_change=(F*percent_SO2_f*10^(-2)*X*(-1)*delta_H_700)/sigma_n_C_pi;//Refer equation 3.60 Pg No.110
+mprintf('\nHeat Capacity evaluated at 800 K :%0.0f (cal/°C)',sigma_n_C_pi);
+mprintf('\nTemperature Change to carry out the reaction at T_F,\nusing the energy to heat the product gas :%0.0f °C",Temp_change);
+//From graphical procedure (Figure 3.19 ,Pg No.118) the final temperature is obtained as 410 °C
+T_F=410;//(°C) Final temperature
+//From Figure 3.19 ,Pg No.118 temperature for corresponding conversion is obtained
+X_stage=[0.1;0.2;0.3;0.4;0.5;0.6]
+T_stage=[441;470;500;540;565;580]
+m=length(X_stage);
+for i=1:m
+ K_eq(i)=exp((11412/T_stage(i))-10.771);
+end
+k=10^-6*[5.25 14.15 27 48 61.5 69];//From Table 3.5 Corresponding to the stage temperature data obtained form Figure 3.19
+for i=1:m
+ P_SO2(i)=11*(1-X_stage(i))*P_opt/(100-5.5*X_stage(i))
+ P_SO3(i)=11*X_stage(i)*P_opt/(100-5.5*X_stage(i))
+ P_O2(i)=10*(10-5.5*X_stage(i))*P_opt/(100-5.5*X_stage(i))
+ r(i)=k(i)*(P_SO2(i)/P_SO3(i))^0.5*(P_O2(i)-(P_SO3(i)/(P_SO2(i)*K_eq(i)))^2)*10^6;
+ inverse_r(i)=(1/r(i));
+end
+scf(1)
+ plot(X_stage,inverse_r,'*');
+ xtitle('1/r vs x','X (conversion)','10^-6/r');
+
+
+//OUTPUT (Ex3.7.a)
+mprintf('\n\n OUTPUT Ex3.7.a');
+mprintf('\n============================================================================');
+mprintf('\n X\tPhi\t\tT_eq\tT_eq\t\tr_max');
+mprintf('\n -\t(atm^-0.5)\t(K)\t(°C)\t\t(gmol/g cat sec)');
+mprintf('\n============================================================================');
+for i=1:n-1
+ mprintf('\n %0.2f\t%0.2f\t %0.0f\t%0.0f\t\t%0.6E',x(i),K_eq(i),T_eq(i),T_eq(i)-273,r_max(i));
+end
+mprintf('\n %0.2f\t%0.2f\t\t%0.0f\t%0.0f\t\t%0.6E',x(n),K_eq(n),T_eq(n),T_eq(n)-273,r_max(n));
+
+//OUTPUT (Ex3.7.b)
+mprintf('\n\n\n OUTPUT Ex3.7.b');
+mprintf('\n============================================================================');
+ mprintf('\n===========================================');
+ mprintf('\n 10^-6/r\tX (conversion)');
+ mprintf('\n (gmol/g cat,s) \t(-)');
+ mprintf('\n===========================================');
+ for i=1:m
+ mprintf('\n %0.2f\t\t\t%0.2f',inverse_r(i),X_stage(i));
+ end
+ mprintf('\nFrom graphical procedure (1/r vs x) the optimum temperature obtained is T_opt: 412°C');
+
+// FILE OUTPUT
+fid= mopen('.\Chapter3-Ex7-Output.txt','w');
+mfprintf(fid,'\nHeat Capacity evaluated at 800 K :%0.0f (cal/°C)',sigma_n_C_pi);
+mfprintf(fid,'\nTemperature Change to carry out the reaction at T_F,\nusing the energy to heat the product gas :%0.0f °C",Temp_change);
+mfprintf(fid,'\n OUTPUT Ex3.7.a');
+mfprintf(fid,'\n============================================================================');
+mfprintf(fid,'\n X\tPhi\t\tT_eq\tT_eq\t\tr_max');
+mfprintf(fid,'\n -\t(atm^-0.5)\t(K)\t(°C)\t\t(gmol/g cat sec)');
+mfprintf(fid,'\n============================================================================');
+for i=1:n-1
+ mfprintf(fid,'\n %0.2f\t%0.2f\t %0.0f\t%0.0f\t\t%0.6E',x(i),K_eq(i),T_eq(i),T_eq(i)-273,r_max(i));
+end
+mfprintf(fid,'\n %0.2f\t%0.2f\t\t%0.0f\t%0.0f\t\t%0.6E',x(n),K_eq(n),T_eq(n),T_eq(n)-273,r_max(n));
+mfprintf(fid,'\n\n\n OUTPUT Ex3.7.b');
+mfprintf(fid,'\n============================================================================');
+ mfprintf(fid,'\n===========================================');
+ mfprintf(fid,'\n 10^-6/r\tX (conversion)');
+ mfprintf(fid,'\n (gmol/g cat,s) \t(-)');
+ mfprintf(fid,'\n===========================================');
+ for i=1:m
+ mfprintf(fid,'\n %0.2f\t\t\t%0.2f',inverse_r(i),X_stage(i));
+ end
+ mfprintf(fid,'\nFrom graphical procedure (1/r vs x) the optimum temperature obtained is T_opt: 412°C');
+ mclose(fid);
+
+//==========================================================END OF PROGRAM======================================
+//Disclaimer: The optimum temperature for each conversion is found by trial at maximum rate and the kinetic data in the textbook is not sufficient to calculate the optimum temperature in the code.
+
generated by cgit (git 2.34.1) at 2024-12-20 04:15:51 +0000