Im trying to solve an equation that have variable on left and right side

How do I solve this equation? I'm giving the important information also.

depth= 1385.33
por=0.153
Qv=0.980
B=3200
Rw=0.265
m=1.86
n=2.2
Rt=4.05
Sw=(Rw/((por^m)*Rt*(1+(B*Qv*Rw)/Sw)))^(1/n)

Answer 1

[John D'Errico]

How is depth relevant to anything here? It does not appear in the expression. Maybe I'm just not thinking very "deeply" today.

If Sw appears on both sides of the equality, surely you can subtract Sw? Just move everything to the same side. WTP?

por=0.153;
Qv=0.980;
B=3200;
Rw=0.265;
m=1.86;
n=2.2;
Rt=4.05;
fun = @(Sw) Sw - (Rw./((por^m)*Rt*(1+(B*Qv*Rw)./Sw))).^(1/n);

Note that for Sw <= 0, you either have a divide by zero at Sw == 0, or a complex result. So If any real solution exists, it must be for positive Sw.

Also note the use of ./ and .^ where necessary in fun. Does a solution exist? PLOT IT!

fplot(fun,[0,0.01])
yline(0);

It looks like a positive solution exists near 0.007.

[Swsol,fval] = fzero(fun,0.007)
Swsol =
       0.00698017018548943
fval =
      8.67361737988404e-19

We could also do this using symbolic tools. No analytical solution will exist because of the non-integer power.

syms Sw
vpasolve(fun(Sw))
ans =
0.006980170185489425081287353

No other positive root will exist. That should be not too difficult to prove.

[Hamid Hamdi]

Yes the depth is no use it is just in my assignment. Actually the Rt has table. It has a lot of values.btw how do you determine the value of 0.01 at the fun? Thank you for you solution!

[Walter Roberson]

If this is a fitting process to determine the optimal Sw, then you would use different code.

You indicate that you have multiple Rt values; for a fitting you would also need multiple values of some other variable -- you need one more more independent variables and one or more dependent variables.

Answer 2

[Ameer Hamza]

This is one of the methods

syms Sw

depth= 1385.33;
por=0.153;
Qv=0.980;
B=3200;
Rw=0.265;
m=1.86;
n=2.2;
Rt=4.05;
eq = Sw==(Rw/((por^m)*Rt*(1+(B*Qv*Rw)/Sw)))^(1/n);

sol = vpasolve(eq, Sw)

[Hamid Hamdi]

Hi Ameer. Thanks for the answer. This is the simple way to understand it. The Rt actually have a lot of values and I'll try to adjust the equation. And I'll try to understand the function u show. Thank you again!

Answer 3

[Walter Roberson]

depth= 1385.33
por=0.153
Qv=0.980
B=3200
Rw=0.265
m=1.86
n=2.2
Rt=4.05
F = @(Sw) (Sw) - ((Rw/((por^m)*Rt*(1+(B*Qv*Rw)/Sw)))^(1/n));
Sw = fsolve(F, 1.234)

[Hamid Hamdi]

I tried this before but it doesn't work.is it because I used the syms fucntion and then used the F. Then I fixed by removing the syms after saw your solution and it gives NaN as answer. Btw how you determine the value of 1.234? Is it random or there is a way to determine it?

[Walter Roberson]

1.234 was an arbitrary starting point.

Answer 4

[N Sudharshan]

clear all        %% solve for SN %%
Z=-1.282;
S=0.5;
PSI=1.9;
M=1000;
W=1000000;
syms SN
eqn = log10(W)==Z*S+9.36*log10(SN+1)-0.20+((log10(PSI/(4.2-1.5)))/(0.40+(1094/(SN+1)^5.19)))+2.32*log10(M)-8.07

eqn = 

solve(eqn)

Warning: Unable to solve symbolically. Returning a numeric solution using vpasolve.

ans = 

6.7204987373948491848493261537531

[Torsten]

Solved.