Errors while trying to setup equation for root finding.

I am trying to set up an equation for root finding to find a, however in the code at the bottom i get an error saying Parse error: Parse error at '=' . usage might be invalid syntax. Does anyone know how to fix this? I'd be grateful for any help.

x_pdo = z_pdo/(1 + a(k_pdo - 1));

x_water = z_water/(1 + a(k_water - 1));

x_glycerol = z_glycerol/(1 + a(k_glycerol - 1));

x_pdo + x_water + x_glycerol - 1 = 0;

[Torsten]

So you have 4 equations. What are the 4 unknowns ?

[Tom Goodland]

all x_... are known, all z_... are known, all k_... are known, the only unknown is a, I am trying to get the function to equal 0 so i can do root finding to calculate a but im not too sure how.

The last equation includes the sum of the first 3 equations - 1 = 0.

[Torsten]

But to determine one variable "a", you only need one equation.

Or do you want to determine "a" such that it satisfies all three equations approximately ?

[Tom Goodland]

I just added the first 3 as a bit of background knowledge so people can see how the x_ was calculated, it is the bottom equation I am trying to use to determine a.

[Torsten]

If you have to insert the first three equations into the last to solve for a, also the x_... are unknown.

Otherwise, you could just pick one of the three equations at the top and solve for a.

[Tom Goodland]

my mistake yeah the x_... are unknown, do you know what function I should use to try to determine a (constant) and x_...? I'm pretty sure fzero would work but I get the error a is an unrecognised function or variable. Do you know any code that would be able to calculate a from the code i've posted as information, if you need anymore information let me know.

Thanks for the help

Answer 1

[James Tursa]

Did you mean multiply by the "a"?

x_pdo = z_pdo/(1 + a*(k_pdo - 1));

x_water = z_water/(1 + a*(k_water - 1));

x_glycerol = z_glycerol/(1 + a*(k_glycerol - 1));

[Tom Goodland]

yes do you have to put the * to multiply a by the bracket?

Answer 2

[Torsten]

function  main
  a0 = 1;
  a = fzero(@fun,a0)
end

function res = fun(a)
  z_pdo = ...;
  k_pdo = ...;
  z_water = ...;
  k_water = ...;
  z_glycerol = ...;
  k_glycerol = ...;
  res = z_pdo/(1 + a*(k_pdo - 1)) + z_water/(1 + a*(k_water - 1)) + z_glycerol/(1 + a*(k_glycerol - 1)) -1.0;
end

[Tom Goodland]

68 function main

69 a0 = 1;

70 a = fzero(@fun,a0);

71 end

72 function res = fun(a)

73 res = z_pdo/(1 + a*(k_pdo - 1)) + z_water/(1 + a*(k_water - 1)) + z_glycerol/(1 + a*(k_glycerol - 1)) -1.0;

74 end

I get 2 errors from this code it says: line 70 the value to variable 'a' might be unused and line 68 the function main might be unused.

I got rid of the k_glycerol = .. etc. because I have already written that higher up the script.

Do you know why these errors are showing up?

Thanks

[Walter Roberson]

Those are both warnings, not errors.

The MATLAB code analyzer encourages the syntax

function  main
  a0 = 1;
  a = fzero(@fun,a0);
  disp(a)
end

[Torsten]

The variables k_...,z_... are not visible in fun - you will have to transfer them to fun from your calling program.

Furthermore, you will have to call main from your program. The code then looks like

function [a] = main(z_pdo,k_pdo,z_water,k_water,z_glycerol,k_glyzerol,a0)
  a = fzero(@(a)fun(a,z_pdo,k_pdo,z_water,k_water,z_glycerol,k_glyzerol),a0)
end

function res = fun(a,z_pdo,k_pdo,z_water,k_water,z_glycerol,k_glyzerol)
  res = z_pdo/(1 + a*(k_pdo - 1)) + z_water/(1 + a*(k_water - 1)) + z_glycerol/(1 + a*(k_glycerol - 1)) -1.0;
end

or you can call fzero directly somewhere in your program:

...
a0 = 1.0;
a = fzero(@(a)fun(a,z_pdo,k_pdo,z_water,k_water,z_glycerol,k_glyzerol),a0)
...
    

Putting z- an k- values in arrays is also an option:

z(1) corresponds to z_pdo, e.g.

z(2) corresponds to z_water, e.g.

z(3) corresponds to z_glycerol, e.g

(same for k)

[Tom Goodland]

I'm still getting the error unrecognised variable or function 'a' on this line: x_pdo = z_pdo/(1 + a*(k_pdo - 1));

I don't know how to fix this as I don't know how to define a without having a value for it. Do you know how?

Thanks

[Torsten]

I'm still getting the error unrecognised variable or function 'a' on this line: x_pdo = z_pdo/(1 + a*(k_pdo - 1));

I don't see this line anywhere in the code I submitted. So I can't give you advice what's going wrong.

[Walter Roberson]

I'm still getting the error unrecognised variable or function 'a' on this line: x_pdo = z_pdo/(1 + a*(k_pdo - 1));

You should not be using that code.

You should either use the symbolic code that I posted, or you should use fsolve of a system of equations,

function residue = fun(xa, z_pdo,k_pdo,z_water,k_water,z_glycerol,k_glyzerol)
    a = x(1);
    x_pdo = x(2);
    x_water = x(3);
    x_gycerol = x(4);
    eqn1 = x_pdo - z_pdo/(1 + a*(k_pdo - 1));
    eqn2 = x_water - z_water/(1 + a*(k_water - 1));
    eqn3 = x_glycerol - z_glycerol/(1 + a*(k_glycerol - 1));
    eqn4 = x_pdo + x_water + x_glycerol - 1;
    residue = [eqn1; eqn2; eqn3; eqn4];
end

[Tom Goodland]

For the first line what is xa i don't see it anywhere else in the code and matlab says it's unused.

Thanks

[Tom Goodland]

Also what should the function 'fun' be and do you know what the function handle should look like? Where should i define the function before calling it in on the top line?

[Torsten]

Why don't you just open a MATLAB session, insert the values for z_... and k_... in "main" and run the below code ? If this does not give you a satisfactory result for "a" or some other problems appear, we can continue discussion.

"fun" is the function the root finder "fzero" expects where you define the equations that are to be solved.

To get used to MATLAB, maybe you should start with

https://de.mathworks.com/learn/tutorials/matlab-onramp.html

function  main
  a0 = 1;
  z_pdo = ...;
  k_pdo = ...;
  z_water = ...;
  k_water = ...;
  z_glycerol = ...;
  k_glycerol = ...;
  a = fzero(@(x)fun(x,k_pdo,k_water,k_glycerol,z_pdo,z_water,z_glycerol),a0)
end
function res = fun(a,k_pdo,k_water,k_glycerol,z_pdo,z_water,z_glycerol)
  res = z_pdo/(1 + a*(k_pdo - 1)) + z_water/(1 + a*(k_water - 1)) + z_glycerol/(1 + a*(k_glycerol - 1)) -1.0;
end

[Walter Roberson]

  %initialize as appropriate
  z_pdo = ...;
  k_pdo = ...;
  z_water = ...;
  k_water = ...;
  z_glycerol = ...;
  k_glycerol = ...;
  
  a0 = ...;
  x_pdo0 = ...;
  x_water0 = ...;
  x_gycerol0 = ...;
  xa0 = [a0, x_pdo0, x_water0, x_gycerol0];
  
  %now do the work
  solution = fsolve(@(xa) fun(xa, z_pdo,k_pdo,z_water,k_water,z_glycerol,k_glyzerol), xa0);

  %results
  a = solution(1)
  x_pdo = solution(2)
  x_water = solution(3)
  x_glycerol = solution(4)
  
function residue = fun(xa, z_pdo,k_pdo,z_water,k_water,z_glycerol,k_glyzerol)
    a = xa(1);
    x_pdo = xa(2);
    x_water = xa(3);
    x_glycerol = xa(4);
    eqn1 = x_pdo - z_pdo/(1 + a*(k_pdo - 1));
    eqn2 = x_water - z_water/(1 + a*(k_water - 1));
    eqn3 = x_glycerol - z_glycerol/(1 + a*(k_glycerol - 1));
    eqn4 = x_pdo + x_water + x_glycerol - 1;
    residue = [eqn1; eqn2; eqn3; eqn4];
end

[Torsten]

@Walter Roberson I think you wanted to use "fsolve" instead of "fzero" in the above code ?

[Walter Roberson]

@Torsten

Yes, you are right, thanks.

[Tom Goodland]

When I ran your code walter matlab said:

Equation solved at initial point.

fsolve completed because the vector of function values at the initial point

is near zero as measured by the value of the function tolerance, and

the problem appears regular as measured by the gradient.

<stopping criteria details>

The x_glycerol, x_pdo etc. were the same values as x_glycerol0, x_pdo0 etc., do I have to set a tspan or something so that it doesn't solve at the initial point?

I would appreciate any help.

Thanks

[Torsten]

If we don't have the missing constants, we can't answer how to do better.

[Tom Goodland]

What are the missing constants? Are you talking about x_glycerol0 etc. and k_glycerol etc. or a and x_glycerol etc.

[Torsten]

The values for the parameters with ... in the code.

[Walter Roberson]

The constants that we are missing are:

z_pdo, k_pdo, z_water, k_water, z_glycerol, k_glycerol

and

a0, x_pdo0, x_water0, x_gycerol0

[Tom Goodland]

z_pdo = 0.015, z_water = 0.975, z_glycerol = 0.01

a0 = 0, x_pdo0 = 0.015, x_water0 = 0.975, x_glycerol = 0.01

k_pdo = 0.1471 k_water = 4.4190 k_glycerol = 177.4713

Thanks

[Torsten]

Yes, this data set gives

a = 0

and

x_pdo = z_pdo , x_water = z_water , x_glycerol = z_glycerol 

using the code from above.

[Tom Goodland]

The feed to the flash unit consists of 1 mol% glycerol, 1.5 mol% PDO and you can assume that the rest is water. The flash evaporator is operated at 2.75 bar and 185 °C.

X_ stands for liquid mole fraction, Z_ stands for mole fraction in the feed. Have I made a mistake in the discussed constants?

𝑥𝑗 = 𝑧𝑗/(1 + 𝛼(𝑘𝑗 − 1))

[Tom Goodland]

α is the vapour to feed ratio (α = FV / FCwhere FC is the feed flow rate and FV is the vapour flow rate)

[Walter Roberson]

if a is the same as α then α(kj-1) is 0 when α is 0, and 1+0 is 1, so xj = zj/stuff would be xj=zj/1...

Answer 3

[Walter Roberson]

syms a k_pdo x_pdo x_glycerol z_pdo z_glycerol k_glycerol k_water x_water z_water
eqn1 = x_pdo == z_pdo/(1 + a*(k_pdo - 1));
eqn2 = x_water == z_water/(1 + a*(k_water - 1));
eqn3 = x_glycerol == z_glycerol/(1 + a*(k_glycerol - 1));
eqn4 = x_pdo + x_water + x_glycerol - 1 == 0;

eqns = [eqn1; eqn2; eqn3; eqn4]

eqns = 

sol = solve(eqns, [a, x_pdo, x_glycerol x_water])

sol = struct with fields:
             a: [3×1 sym]
         x_pdo: [3×1 sym]
    x_glycerol: [3×1 sym]
       x_water: [3×1 sym]

sols = [sol.a, sol.x_pdo, sol.x_glycerol, sol.x_water]

sols = 

sol3 = solve(eqns, [a, x_pdo, x_glycerol x_water], 'maxdegree', 3);
sol3s = [sol3.a, sol3.x_pdo, sol3.x_glycerol, sol3.x_water];
vpa(sol3s)

ans =