Maximizing Batch Reactor Products in matlab

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naiva saeedia
naiva saeedia 2023-8-1
编辑： naiva saeedia 2023-8-2
Hi..I want to maximize W_C10 which is the mass concentraion of C10 products in a batch Reactor...And what I meant by maximization is W_C10 is going to be greater than all the other W_Ci,i=4,6,..,20..Here is my constraints for T,C_TEA and C_CAT and C_M:
338.15=<T=<368.15
1=<C_TEA<=200
1=<C_M<=100
C_CAT=x*C_TEA where x=17,18,...,45
Here is my ode system to solve W_Cis..Can someone help me to do this?
clc
clear
close all
T= 3.642755276270583e2;
T_r=273.15+0;
A1=4.525e5;
E1 =3985.;
A2 = 0.5101e9;
E2 = 52670.;
A3 = 0.4949e9;
E3 = 15140.;
A4 = 465000.;
E4 = 14330.;
A5 = 1.255;
E5 = 0;
R = 1.98;
k1 = A1*exp(E1*(1/T - 1/T_r)/R);
k2 = A2*exp(E2*(1/T - 1/T_r)/R);
k3 = A3*exp(E3*(1/T - 1/T_r)/R);
k4 = A4*exp(E4*(1/T - 1/T_r)/R);
k5 = A5*exp(E5*(1/T - 1/T_r)/R);
KA = 481.2;
KB = 277.1;
KC = 6906;
KD = 40830;
KE = 59.55;
C_M= 46.946030544906776;
C_TEA=1.022918116483290e2;
C_CAT=45*C_TEA;
C_M_K=C_M/(KB*C_TEA+1);
C_CAT_K=C_CAT/(KA*C_M+1);
C_TEA_k=C_TEA/(KC*C_CAT+1)^2;
dCdt=@(t,x) [k1.*C_CAT_K.*C_M_K-k2.*x(1).*C_M-k5.*x(1);k2.*C_M.*x(1)-(k3.*x(2).*C_M)./(KD.*C_TEA+1)-k5.*x(2);(k3.*x(2).*C_M)./(KD.*C_TEA+1)-(k3.*x(3).*C_M)./(KD.*C_TEA+1)-k5.*x(3);(k3.*x(3).*C_M)./(KD.*C_TEA+1)-(k3.*x(4).*C_M)./(KD.*C_TEA+1)-k5.*x(4);(k3.*x(4).*C_M)./(KD.*C_TEA+1)-(k3.*x(5).*C_M)./(KD.*C_TEA+1)-k5.*x(5);(k3.*x(5).*C_M)./(KD.*C_TEA+1)-(k3.*x(6).*C_M)./(KD.*C_TEA+1)-k5.*x(6);(k3.*x(6).*C_M)./(KD.*C_TEA+1)-(k3.*x(7).*C_M)./(KD.*C_TEA+1)-k5.*x(7);(k3.*x(7).*C_M)./(KD.*C_TEA+1)-(k3.*x(8).*C_M)./(KD.*C_TEA+1)-k5.*x(8);(k3.*x(8).*C_M)./(KD.*C_TEA+1)-(k3.*x(9).*C_M)./(KD.*C_TEA+1)-k5.*x(9);(k3.*x(9).*C_M)./(KD.*C_TEA+1)-(k3.*x(10).*C_M)./(KD.*C_TEA+1)-k5.*x(10);(k3.*x(10).*C_M)./(KD.*C_TEA+1)-(k3.*x(11).*C_M)./(KD.*C_TEA+1)-k5.*x(11);(k4.*x(3).*C_M)./(KE.*C_TEA+1)+k5.*x(3);(k4.*x(4).*C_M)./(KE.*C_TEA+1)+k5.*x(4);(k4.*x(5).*C_M)./(KE.*C_TEA+1)+k5.*x(5);(k4.*x(6).*C_M)./(KE.*C_TEA+1)+k5.*x(6);(k4.*x(7).*C_M)./(KE.*C_TEA+1)+k5.*x(7);(k4.*x(8).*C_M)./(KE.*C_TEA+1)+k5.*x(8);(k4.*x(9).*C_M)./(KE.*C_TEA+1)+k5.*x(9);(k4.*x(10).*C_M)./(KE.*C_TEA+1)+k5.*x(10);(k4.*x(11).*C_M)./(KE.*C_TEA+1)+k5.*x(11);k5.*(x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)+x(9)+x(10)+x(11))];
[t,x]=ode45(dCdt,[0,3600],[0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0]);
%Moles Disturbutions in dead chains
t1=3600;
M_total=x(t1,12)+x(t1,13)+x(t1,14)+x(t1,15)+x(t1,16)+x(t1,17)+x(t1,18)+x(t1,19)+x(t1,20);
M_C4=x(t1,12)/M_total;
M_C6=x(t1,13)/M_total;
M_C8=x(t1,14)/M_total;
M_C10=x(t1,15)/M_total;
M_C12=x(t1,16)/M_total;
M_C14=x(t1,17)/M_total;
M_C16=x(t1,18)/M_total;
M_C18=x(t1,19)/M_total;
M_C20=x(t1,20)/M_total;
T1=table(M_C4,M_C6,M_C8,M_C10,M_C12,M_C14,M_C16,M_C18,M_C20)
%Mass Disturbutions in dead chains Basis=100mole
W_total=100*M_C4*72+100*M_C6*84+100*M_C8*112+100*M_C10*140+100*M_C12*168+100*M_C14*196+100*M_C16*224+100*M_C18*252+100*M_C20*280;
W_C4=100*M_C4*72/W_total;
W_C6=100*M_C6*84/W_total;
W_C8=100*M_C8*112/W_total;
W_C10=100*M_C10*140/W_total;
W_C12=100*M_C12*168/W_total;
W_C14=100*M_C14*196/W_total;
W_C16=100*M_C16*224/W_total;
W_C18=100*M_C18*252/W_total;
W_C20=100*M_C20*280/W_total;
T2=table(W_C4,W_C6,W_C8,W_C10,W_C12,W_C14,W_C16,W_C18,W_C20)
a=[W_C4,W_C6,W_C8,W_C10,W_C12,W_C14,W_C16,W_C18,W_C20]

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采纳的回答

Torsten
Torsten 2023-8-2
编辑：Torsten 2023-8-2
Ran in:
You get almost identical values for the optimal T, C_M and C_TEA for all x-values in between 17 and 45 as you can see after the first loop in the code.
By strengthening the tolerances, now W_C4 is also smaller than W_C10 in all cases.
"obj" sets the function to be maximized - in this case I chose W_C10.
"constr" defines the constraints under which the function in "obj" is maximized. In this case, I chose W_Ci - W_C10 <= 0 for i = 4,6,...,20.
The code can be rearranged to look smarter (e.g. the threefold repetition of the calculation of the M_Ci ang W_Ci should be put in its own function) - I leave these technical changes to you.
x = 17:45;
for i = 1:numel(x)
lb = [338.15;1;1];
ub = [368.15;100;200];
p0 = (lb+ub)/2;
options = optimoptions('fmincon','Display','off','Algorithm','interior-point','ConstraintTolerance',1e-16);
[p,fval,exitflag,~] = fmincon(@(p)obj(p,x(i)),p0,[],[],[],[],lb,ub,@(p)constr(p,x(i)),options);
T_opt(i) = p(1);
C_M_opt(i) = p(2);
C_TEA_opt(i) = p(3);
C_CAT_opt(i) = C_TEA_opt(i)*x(i);
value_opt(i) = -fval;
exit(i) = exitflag;
end
exit
exit = 1×29
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
T_opt
T_opt = 1×29
364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755 364.2755
C_M_opt
C_M_opt = 1×29
46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460 46.9460
C_TEA_opt
C_TEA_opt = 1×29
102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918 102.2918
C_CAT_opt
C_CAT_opt = 1×29
1.0e+03 * 1.7390 1.8413 1.9435 2.0458 2.1481 2.2504 2.3527 2.4550 2.5573 2.6596 2.7619 2.8642 2.9665 3.0688 3.1710 3.2733 3.3756 3.4779 3.5802 3.6825 3.7848 3.8871 3.9894 4.0917 4.1940 4.2963 4.3985 4.5008 4.6031
value_opt
value_opt = 1×29
0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247 0.1247
%Postprocess results
for i = 1:numel(x)
[t,x] = ode_solution([T_opt(i),C_M_opt(i),C_TEA_opt(i)],x(i));
M_total=x(end,12)+x(end,13)+x(end,14)+x(end,15)+x(end,16)+x(end,17)+x(end,18)+x(end,19)+x(end,20);
M_C4=x(end,12)/M_total;
M_C6=x(end,13)/M_total;
M_C8=x(end,14)/M_total;
M_C10=x(end,15)/M_total;
M_C12=x(end,16)/M_total;
M_C14=x(end,17)/M_total;
M_C16=x(end,18)/M_total;
M_C18=x(end,19)/M_total;
M_C20=x(end,20)/M_total;
%Mass Disturbutions in dead chains Basis=100mole
W_total=100*M_C4*72+100*M_C6*84+100*M_C8*112+100*M_C10*140+100*M_C12*168+100*M_C14*196+100*M_C16*224+100*M_C18*252+100*M_C20*280;
W_C4(i)=100*M_C4*72/W_total;
W_C6(i)=100*M_C6*84/W_total;
W_C8(i)=100*M_C8*112/W_total;
W_C10(i)=100*M_C10*140/W_total;
W_C12(i)=100*M_C12*168/W_total;
W_C14(i)=100*M_C14*196/W_total;
W_C16(i)=100*M_C16*224/W_total;
W_C18(i)=100*M_C18*252/W_total;
W_C20(i)=100*M_C20*280/W_total;
end
any(W_C4>=W_C10)
ans = logical
0
any(W_C6>=W_C10)
ans = logical
0
any(W_C8>=W_C10)
ans = logical
0
any(W_C12>=W_C10)
ans = logical
0
any(W_C14>=W_C10)
ans = logical
0
any(W_C16>=W_C10)
ans = logical
0
any(W_C18>=W_C10)
ans = logical
0
any(W_C20>=W_C10)
ans = logical
0
function value = obj(p,factor)
[t,x] = ode_solution(p,factor);
M_total=x(end,12)+x(end,13)+x(end,14)+x(end,15)+x(end,16)+x(end,17)+x(end,18)+x(end,19)+x(end,20);
M_C4=x(end,12)/M_total;
M_C6=x(end,13)/M_total;
M_C8=x(end,14)/M_total;
M_C10=x(end,15)/M_total;
M_C12=x(end,16)/M_total;
M_C14=x(end,17)/M_total;
M_C16=x(end,18)/M_total;
M_C18=x(end,19)/M_total;
M_C20=x(end,20)/M_total;
%Mass Disturbutions in dead chains Basis=100mole
W_total=100*M_C4*72+100*M_C6*84+100*M_C8*112+100*M_C10*140+100*M_C12*168+100*M_C14*196+100*M_C16*224+100*M_C18*252+100*M_C20*280;
W_C4=100*M_C4*72/W_total;
W_C6=100*M_C6*84/W_total;
W_C8=100*M_C8*112/W_total;
W_C10=100*M_C10*140/W_total;
W_C12=100*M_C12*168/W_total;
W_C14=100*M_C14*196/W_total;
W_C16=100*M_C16*224/W_total;
W_C18=100*M_C18*252/W_total;
W_C20=100*M_C20*280/W_total;
value = -W_C10;
end
function [c,ceq] = constr(p,factor)
[t,x] = ode_solution(p,factor);
M_total=x(end,12)+x(end,13)+x(end,14)+x(end,15)+x(end,16)+x(end,17)+x(end,18)+x(end,19)+x(end,20);
M_C4=x(end,12)/M_total;
M_C6=x(end,13)/M_total;
M_C8=x(end,14)/M_total;
M_C10=x(end,15)/M_total;
M_C12=x(end,16)/M_total;
M_C14=x(end,17)/M_total;
M_C16=x(end,18)/M_total;
M_C18=x(end,19)/M_total;
M_C20=x(end,20)/M_total;
%Mass Disturbutions in dead chains Basis=100mole
W_total=100*M_C4*72+100*M_C6*84+100*M_C8*112+100*M_C10*140+100*M_C12*168+100*M_C14*196+100*M_C16*224+100*M_C18*252+100*M_C20*280;
W_C4=100*M_C4*72/W_total;
W_C6=100*M_C6*84/W_total;
W_C8=100*M_C8*112/W_total;
W_C10=100*M_C10*140/W_total;
W_C12=100*M_C12*168/W_total;
W_C14=100*M_C14*196/W_total;
W_C16=100*M_C16*224/W_total;
W_C18=100*M_C18*252/W_total;
W_C20=100*M_C20*280/W_total;
c(1) = W_C4 - W_C10;
c(2) = W_C6 - W_C10;
c(3) = W_C8 - W_C10;
c(4) = W_C12 - W_C10;
c(5) = W_C14 - W_C10;
c(6) = W_C16 - W_C10;
c(7) = W_C18 - W_C10;
c(8) = W_C20 - W_C10;
ceq = [];
end
function [t,x] = ode_solution(p,factor)
T=p(1);
C_M=p(2);
C_TEA=p(3);
C_CAT = factor*C_TEA;
T_r=273.15+0;
A1=4.525e5;
E1 =3985.;
A2 = 0.5101e9;
E2 = 52670.;
A3 = 0.4949e9;
E3 = 15140.;
A4 = 465000.;
E4 = 14330.;
A5 = 1.255;
E5 = 0;
R = 1.98;
k1 = A1*exp(E1*(1/T - 1/T_r)/R);
k2 = A2*exp(E2*(1/T - 1/T_r)/R);
k3 = A3*exp(E3*(1/T - 1/T_r)/R);
k4 = A4*exp(E4*(1/T - 1/T_r)/R);
k5 = A5*exp(E5*(1/T - 1/T_r)/R);
KA = 481.2;
KB = 277.1;
KC = 6906;
KD = 40830;
KE = 59.55;
C_M_K=C_M/(KB*C_TEA+1);
C_CAT_K=C_CAT/(KA*C_M+1);
C_TEA_k=C_TEA/(KC*C_CAT+1)^2;
dCdt=@(t,x) [k1.*C_CAT_K.*C_M_K-k2.*x(1).*C_M-k5.*x(1);k2.*C_M.*x(1)-(k3.*x(2).*C_M)./(KD.*C_TEA+1)-k5.*x(2);(k3.*x(2).*C_M)./(KD.*C_TEA+1)-(k3.*x(3).*C_M)./(KD.*C_TEA+1)-k5.*x(3);(k3.*x(3).*C_M)./(KD.*C_TEA+1)-(k3.*x(4).*C_M)./(KD.*C_TEA+1)-k5.*x(4);(k3.*x(4).*C_M)./(KD.*C_TEA+1)-(k3.*x(5).*C_M)./(KD.*C_TEA+1)-k5.*x(5);(k3.*x(5).*C_M)./(KD.*C_TEA+1)-(k3.*x(6).*C_M)./(KD.*C_TEA+1)-k5.*x(6);(k3.*x(6).*C_M)./(KD.*C_TEA+1)-(k3.*x(7).*C_M)./(KD.*C_TEA+1)-k5.*x(7);(k3.*x(7).*C_M)./(KD.*C_TEA+1)-(k3.*x(8).*C_M)./(KD.*C_TEA+1)-k5.*x(8);(k3.*x(8).*C_M)./(KD.*C_TEA+1)-(k3.*x(9).*C_M)./(KD.*C_TEA+1)-k5.*x(9);(k3.*x(9).*C_M)./(KD.*C_TEA+1)-(k3.*x(10).*C_M)./(KD.*C_TEA+1)-k5.*x(10);(k3.*x(10).*C_M)./(KD.*C_TEA+1)-(k3.*x(11).*C_M)./(KD.*C_TEA+1)-k5.*x(11);(k4.*x(3).*C_M)./(KE.*C_TEA+1)+k5.*x(3);(k4.*x(4).*C_M)./(KE.*C_TEA+1)+k5.*x(4);(k4.*x(5).*C_M)./(KE.*C_TEA+1)+k5.*x(5);(k4.*x(6).*C_M)./(KE.*C_TEA+1)+k5.*x(6);(k4.*x(7).*C_M)./(KE.*C_TEA+1)+k5.*x(7);(k4.*x(8).*C_M)./(KE.*C_TEA+1)+k5.*x(8);(k4.*x(9).*C_M)./(KE.*C_TEA+1)+k5.*x(9);(k4.*x(10).*C_M)./(KE.*C_TEA+1)+k5.*x(10);(k4.*x(11).*C_M)./(KE.*C_TEA+1)+k5.*x(11);k5.*(x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)+x(9)+x(10)+x(11))];
[t,x]=ode15s(dCdt,[0,3600],[0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0],odeset('AbsTol',1e-10,'RelTol',1e-10));
end
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显示 1更早的评论
Torsten
Torsten 2023-8-2
编辑：Torsten 2023-8-2
It's not possible. Assume you want to minimize x^2 over x > 0. Then no optimal x exists. Only if you choose the constraint as x>=0, you get x=0 as solution.
This generalizes to the domains over which optimization is performed in general. It has to be always closed (<=), not open (<0).
But I changed the checks to any(W_Ci>=W_C10) in the above code, and as you can see: all constraints are satisfied in the strict sense (W_Ci < W_C10).

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更多回答（1 个）

Torsten
Torsten 2023-8-1
编辑：Torsten 2023-8-1
Ran in:
max_value = -Inf;
T_array = linspace(338.15,368.15,10);
C_M_array = linspace(1,100,10);
C_TEA_array = linspace(1,200,10);
C_CAT_array = linspace(17,400,10);
for i = 1:numel(T_array)
T = T_array(i);
for j = 1:numel(C_M_array)
C_M = C_M_array(j);
for k = 1:numel(C_TEA_array)
C_TEA = C_TEA_array(k);
for l = 1:numel(C_CAT_array)
C_CAT = C_CAT_array(l);
T_r=273.15+0;
A1=4.525e5;
E1 =3985.;
A2 = 0.5101e9;
E2 = 52670.;
A3 = 0.4949e9;
E3 = 15140.;
A4 = 465000.;
E4 = 14330.;
A5 = 1.255;
E5 = 0;
R = 1.98;
k1 = A1*exp(E1*(1/T - 1/T_r)/R);
k2 = A2*exp(E2*(1/T - 1/T_r)/R);
k3 = A3*exp(E3*(1/T - 1/T_r)/R);
k4 = A4*exp(E4*(1/T - 1/T_r)/R);
k5 = A5*exp(E5*(1/T - 1/T_r)/R);
KA = 481.2;
KB = 277.1;
KC = 6906;
KD = 40830;
KE = 59.55;
C_M_K=C_M/(KB*C_TEA+1);
C_CAT_K=C_CAT/(KA*C_M+1);
C_TEA_k=C_TEA/(KC*C_CAT+1)^2;
dCdt=@(t,x) [k1.*C_CAT_K.*C_M_K-k2.*x(1).*C_M-k5.*x(1);k2.*C_M.*x(1)-(k3.*x(2).*C_M)./(KD.*C_TEA+1)-k5.*x(2);(k3.*x(2).*C_M)./(KD.*C_TEA+1)-(k3.*x(3).*C_M)./(KD.*C_TEA+1)-k5.*x(3);(k3.*x(3).*C_M)./(KD.*C_TEA+1)-(k3.*x(4).*C_M)./(KD.*C_TEA+1)-k5.*x(4);(k3.*x(4).*C_M)./(KD.*C_TEA+1)-(k3.*x(5).*C_M)./(KD.*C_TEA+1)-k5.*x(5);(k3.*x(5).*C_M)./(KD.*C_TEA+1)-(k3.*x(6).*C_M)./(KD.*C_TEA+1)-k5.*x(6);(k3.*x(6).*C_M)./(KD.*C_TEA+1)-(k3.*x(7).*C_M)./(KD.*C_TEA+1)-k5.*x(7);(k3.*x(7).*C_M)./(KD.*C_TEA+1)-(k3.*x(8).*C_M)./(KD.*C_TEA+1)-k5.*x(8);(k3.*x(8).*C_M)./(KD.*C_TEA+1)-(k3.*x(9).*C_M)./(KD.*C_TEA+1)-k5.*x(9);(k3.*x(9).*C_M)./(KD.*C_TEA+1)-(k3.*x(10).*C_M)./(KD.*C_TEA+1)-k5.*x(10);(k3.*x(10).*C_M)./(KD.*C_TEA+1)-(k3.*x(11).*C_M)./(KD.*C_TEA+1)-k5.*x(11);(k4.*x(3).*C_M)./(KE.*C_TEA+1)+k5.*x(3);(k4.*x(4).*C_M)./(KE.*C_TEA+1)+k5.*x(4);(k4.*x(5).*C_M)./(KE.*C_TEA+1)+k5.*x(5);(k4.*x(6).*C_M)./(KE.*C_TEA+1)+k5.*x(6);(k4.*x(7).*C_M)./(KE.*C_TEA+1)+k5.*x(7);(k4.*x(8).*C_M)./(KE.*C_TEA+1)+k5.*x(8);(k4.*x(9).*C_M)./(KE.*C_TEA+1)+k5.*x(9);(k4.*x(10).*C_M)./(KE.*C_TEA+1)+k5.*x(10);(k4.*x(11).*C_M)./(KE.*C_TEA+1)+k5.*x(11);k5.*(x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)+x(9)+x(10)+x(11))];
[t,x]=ode15s(dCdt,[0,3600],[0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0]);
if x(end,15) > max_value
I = i;
J = j;
K = k;
L = l;
max_value = x(end,15);
end
end
end
end
end
T_array(I)
ans = 338.1500
C_M_array(J)
ans = 100
C_TEA_array(K)
ans = 1
C_CAT_array(L)
ans = 400
max_value
max_value = 9.9395e+05
  13 个评论
显示 11更早的评论
naiva saeedia
naiva saeedia 2023-8-2
Wow..tnx a lot and Yeah it didn't have WC2 sorry for the mistake...Can we find what's the value of factor or C_CAT is here?
naiva saeedia
naiva saeedia 2023-8-2
编辑：naiva saeedia 2023-8-2
Never mind...the value of factor is 29 right?...there is a little problem and I don't know why this is happening...I tried the value that your code is giving me in my code to find out WCi's values but as u can see WC4 is greater than WC10
Why this is happening? Every other WCis are lesser than the WC10 and WC4 is the only value that is greater than W_C10...I also didn't understand what Constr and Obj functions are doing so If u could give me some explanation that would be great(especially when u defined C(1),..,C(8) in Constr and value part in Obj function) and tnq for ur time and effort what u did is pretty amazing!

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