Hi, I have been trying to carry out the mole balance of certain reactions on excel, but the equations have refused to converge, hence my switch to matlab.

I have represented the variables (#moles of certain gases) I want to calculate by x(1) - x(5),

These are the set of equations I formulated. It seems pretty straightforward but I'm not getting the results I desire.

close all, clear all, clc, format compact
x0 = [0,0,0,0,0,0]; %initial guess values
fun = @eqns_J;
options = optimoptions('fsolve','Display','iter','StepTolerance',1e-14,'MaxFunctionEvaluations',5000,'MaxIterations',2000)
x = fsolve(fun,x0,options)
%These are the equations I want to solve, and I don't want any of the solutions to be negative
function F = eqns_J(x);
F(1) = x(3)+x(1)-0.3995;
F(2) = (4*x(1))+(2*x(2))+(2*x(4))-0.6519;
F(3) = x(2)+(2*x(3))-0.03788;
F(4) = x(5)-0.005449;
F(5) = 6.314 - ((x(1)*16.042)+(x(2)*18.016)+(x(3)*44.010)+(x(4)*34.086)+(x(5)*28.020));
end

With this code I'm getting a solution but with a negative x(2).

I saw some suggestions on here that Ican try fmincon and I did, but it still doesn't converge;

function massbalance_const
close all, clear all, clc, format compact
x0 = [0.5;0.1;0.7;0.4;0.1]; %initial guess values
A = [];
b = [];
Aeq = [1 0 1 0 0 ; 4 2 0 2 0; 0 1 2 0 0; 0 0 0 1 0; 0 0 0 0 1]; %equality constraints equations for the mole balances
beq = [0.3995; 0.6519; 0.0379; 0.0055; 0.0054];
lb = zeros(1,5);
ub = inf(1,5);
nonlcon = [];
options = optimoptions('fmincon','Algorithm','sqp','Display','iter','ConstraintTolerance',1e-30,'StepTolerance',1e-30);;

x = fmincon(@fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)

function f = fun(x)
f = 6.314-((x(1)*16.042)+(x(2)*18.016)+(x(3)*44.010)+(x(4)*34.086)+(x(5)*28.020));
end
end

I also tried increasing the iterations, but it doesn't converge and the solution it outputs does not satisfy the mole balance equations I have. .

Any suggestions, help and advice on how best I can modify the solution would be really appreciated.

Thank you!

[Rik]

Two things:

1. Your question is not urgent, the reason for that is explained here.
2. How did you make sure these equations converge at all?

Have a read here and here. It will greatly improve your chances of getting an answer.

[Chiderah Chukwuka]

Hi Rik, thanks for correcting my manner of approach. I hope I've been able to make the necessary edits to the frame of the question.

[Rik]

Your edits improved the question already. I still don't see why your assumption is valid. How are you sure that there exists a solution at all?

This will not help anything, but you should remove the "close all, clear all, clc". You're already using a function to keep your workspace clean and you're not using any figures, so closing them is not needed.

[Chiderah Chukwuka]

Thank you, I tried that but still no convergence. I'm guessing the issue can be traced to the assumptions (data) that I'm using, thanks for pointing that out.

Answer 1

[Alan Weiss]

You have a set of linear equations. You can represent your equations in terms of a matrix A and vector b in the usual framework

% A*x = b

with the following entries:

A = [1 0 1 0 0
    4 2 0 2 0
    0 1 2 0 0
    0 0 0 0 1
    16.042 18.016 44.010 34.086 28.020];
b = [0.3995
    0.6519
    0.03788
    0.005449
    6.314];

You get the solution using backslash:

x = A\b

x = 5×1

0.2710 -0.2191 0.1285 0.0031 0.0054

You can check whether other solutions might exist by checking if the determinant of A is zero:

det(A)

ans = -256.5600

The determinant is not zero, so the solution is unique. In other words, there is exactly one solution to your system of equations, and it has a negative value of x(2).

Alan Weiss

MATLAB mathematical toolbox documentation

[Chiderah Chukwuka]

Thank you. This definitely makes sense, I guess I have to go back to the drawing board and crosscheck all the data I'm using for accuracy.