Why my result is 0×1 empty double column vector

function[u_g] = viscosity(Pm) % viscosity() calculates viscosity of the gas at given reservoir % temperature and pressure.
M_air=[28.96;29;29.56;30;31;31.86;32;32.3;33;33.50];
Avg_Mol_Wt= [25.48;26;26.12;26.79;27;27.60;28;29;29.40;30];
spgr=Avg_Mol_Wt.\M_air;
Pm=[3800;3850;3400;3450;3500;3550;3600;3650;3700;3750]; %initial reservoir pressure

T=[660;680;720;740;760;780;800;820;840;860];  %Reservoir Temperature= 660 deg R (Literature)
u_uncorrected = ((1.709 * (10^(-5)-(2.062*10^(-6)*spgr))).*(T-460))+((8.118*10^(-3))-(6.15*10^(-3)*log10(spgr)));
yCO2 = 0.03;
yN2 = 0.02;
yH2S = 0.01;
u_CO2 = (yCO2*(((9.08*10^(-3))*(log10(spgr)))+ (6.24*10^(-3))));
u_N2 = (yN2*((8.48*10^(-3)*log10(spgr))+ (9.59*10^(-3))));
u_H2S = (yH2S*((8.49*10^(-3)*log10(spgr))+ (3.73*10^(-3))));
u1 = u_uncorrected + u_CO2 + u_N2 + u_H2S ;
Tpc = 168 + (325 * spgr) -(12.5*(spgr.^2)); 
Ppc = 677 + (15*spgr) -(37.5*(spgr.^2)); 
Tpr = T/Tpc;
Ppr = Pm/Ppc;
% Constants for viscosity relation 
a0 = -2.4621182; 
a1 = 2.970547414;
a2 = -0.286264054; 
a3 = 0.008054205;
a4 = 2.80860949; 
a5 = -3.49803305;
a6 = 0.36037302; 
a7 = -0.01044324;
a8 = -0.793385648;
a9 = 1.39643306; 
a10 = -0.149144925; 
a11 = 0.004410155; 
a12 = 0.083938718; 
a13 = -0.186408848;
a14 =0.020336788; 
a15 = -0.000609579;
syms ug;
con = a0+(a1.*Ppr)+(a2.*(Ppr.^2))+ (a3.*(Ppr.^3)) +(Tpr.*(a4+(a5.*Ppr)+(a6.*Ppr.^2)+(a7.*Ppr.^3)))+((Tpr.^2)*(a8+(a9.*Ppr)+(a10.*Ppr.^2)+(a11.*Ppr.^3)))+((Tpr.^3)*(a12+(a13.*Ppr)+(a14.*Ppr.^2)+(a15.*Ppr.^3)));
eqn = ((Tpr.*ug) == u1.*exp(con));
temp = solve(eqn,'ug');
u_g = double(temp);
end

results

>> viscosity

Warning: Do not specify equations and variables as

character vectors. Instead, create symbolic variables

with syms.

> In solve>getEqns (line 446)

In solve (line 226)

In viscosity (line 40)

ans =

0×1 empty double column vector

Answer 1

[John D'Errico]

Um, LOOK AT WHAT YOU DID?

eqn
eqn =
[ 0 == 5780664229092589/18446744073709551616, 0 == 5780664229092589/18446744073709551616, 0 == 5780664229092589/18446744073709551616, 0 == 5780664229092589/18446744073709551616, 0 == 5780664229092589/18446744073709551616, (5645467684136263*ug)/4503599627370496 == 3053705270954071/288230376151711744, 0 == 5780664229092589/18446744073709551616, 0 == 4586793404289899/8796093022208, 0 == 5780664229092589/18446744073709551616, 0 == 5780664229092589/18446744073709551616]
[ 0 == 5600019709277477/18446744073709551616, 0 == 5600019709277477/18446744073709551616, 0 == 5600019709277477/18446744073709551616, 0 == 5600019709277477/18446744073709551616, 0 == 5600019709277477/18446744073709551616,   (5816542462443423*ug)/4503599627370496 == 822835767405345/72057594037927936, 0 == 5600019709277477/18446744073709551616, 0 == 3047385662287835/4398046511104, 0 == 5600019709277477/18446744073709551616, 0 == 5600019709277477/18446744073709551616]
[  0 == 2572630575198711/9223372036854775808,  0 == 2572630575198711/9223372036854775808,  0 == 2572630575198711/9223372036854775808,  0 == 2572630575198711/9223372036854775808,  0 == 2572630575198711/9223372036854775808, (3079346009528871*ug)/2251799813685248 == 7486683279545443/576460752303423488,  0 == 2572630575198711/9223372036854775808, 0 == 1741669557772335/2199023255552,  0 == 2572630575198711/9223372036854775808,  0 == 2572630575198711/9223372036854775808]
[  0 == 2472319987732461/9223372036854775808,  0 == 2472319987732461/9223372036854775808,  0 == 2472319987732461/9223372036854775808,  0 == 2472319987732461/9223372036854775808,  0 == 2472319987732461/9223372036854775808, (6329766797364901*ug)/4503599627370496 == 4002404158088997/288230376151711744,  0 == 2472319987732461/9223372036854775808, 0 == 4733878050545925/4398046511104,  0 == 2472319987732461/9223372036854775808,  0 == 2472319987732461/9223372036854775808]
[  0 == 2346687901508061/9223372036854775808,  0 == 2346687901508061/9223372036854775808,  0 == 2346687901508061/9223372036854775808,  0 == 2346687901508061/9223372036854775808,  0 == 2346687901508061/9223372036854775808, (6500841575672061*ug)/4503599627370496 == 8453485532814763/576460752303423488,  0 == 2346687901508061/9223372036854775808, 0 == 1593573526385771/1099511627776,  0 == 2346687901508061/9223372036854775808,  0 == 2346687901508061/9223372036854775808]
[ 0 == 8946768155106723/36893488147419103232, 0 == 8946768155106723/36893488147419103232, 0 == 8946768155106723/36893488147419103232, 0 == 8946768155106723/36893488147419103232, 0 == 8946768155106723/36893488147419103232, (1667979088494805*ug)/1125899906842624 == 8964393129251763/576460752303423488, 0 == 8946768155106723/36893488147419103232,  0 == 1080598422980285/549755813888, 0 == 8946768155106723/36893488147419103232, 0 == 8946768155106723/36893488147419103232]
[  0 == 1069123269945641/4611686018427387904,  0 == 1069123269945641/4611686018427387904,  0 == 1069123269945641/4611686018427387904,  0 == 1069123269945641/4611686018427387904,  0 == 1069123269945641/4611686018427387904, (1710747783071595*ug)/1125899906842624 == 4767346375255051/288230376151711744,  0 == 1069123269945641/4611686018427387904, 0 == 2948226993291101/1099511627776,  0 == 1069123269945641/4611686018427387904,  0 == 1069123269945641/4611686018427387904]
[ 0 == 4100813596974095/18446744073709551616, 0 == 4100813596974095/18446744073709551616, 0 == 4100813596974095/18446744073709551616, 0 == 4100813596974095/18446744073709551616, 0 == 4100813596974095/18446744073709551616,   (7014065910593539*ug)/4503599627370496 == 317887318073797/18014398509481984, 0 == 4100813596974095/18446744073709551616, 0 == 4045185938083311/1099511627776, 0 == 4100813596974095/18446744073709551616, 0 == 4100813596974095/18446744073709551616]
[ 0 == 7774278768879437/36893488147419103232, 0 == 7774278768879437/36893488147419103232, 0 == 7774278768879437/36893488147419103232, 0 == 7774278768879437/36893488147419103232, 0 == 7774278768879437/36893488147419103232,   (7185140688900699*ug)/4503599627370496 == 670498029164941/36028797018963968, 0 == 7774278768879437/36893488147419103232,  0 == 2750305037577659/549755813888, 0 == 7774278768879437/36893488147419103232, 0 == 7774278768879437/36893488147419103232]
[  0 == 1846563996020195/9223372036854775808,  0 == 1846563996020195/9223372036854775808,  0 == 1846563996020195/9223372036854775808,  0 == 1846563996020195/9223372036854775808,  0 == 1846563996020195/9223372036854775808,   (3678107733603929*ug)/2251799813685248 == 354377367836401/18014398509481984,  0 == 1846563996020195/9223372036854775808, 0 == 7515208335023383/1099511627776,  0 == 1846563996020195/9223372036854775808,  0 == 1846563996020195/9223372036854775808]

So, most of that mess is of a form like this:

eqn(1)
ans =
0 == 5780664229092589/18446744073709551616

Which value of ug will satisfy that EXACTLY? Yeah, right. It looks like there will never be a solution to what you are doing. Not that we are given a hint as to what you really need to do, which is probably not what you actually wrote code to do since that system of equations is meaningless.

So, why is your result an empty vector? Because there is no solution to what you posed.

[Walter Roberson]

Perhaps they had intended to do a fitting.

[John D'Errico]

They MIGHT have wanted to do so.

Answer 2

[Walter Roberson]

function[u_g] = viscosity(Pm) % viscosity() calculates viscosity of the gas at given reservoir % temperature and pressure.
M_air=[28.96;29;29.56;30;31;31.86;32;32.3;33;33.50];
Avg_Mol_Wt= [25.48;26;26.12;26.79;27;27.60;28;29;29.40;30];
spgr=Avg_Mol_Wt.\M_air;
Pm=[3800;3850;3400;3450;3500;3550;3600;3650;3700;3750]; %initial reservoir pressure
T=[660;680;720;740;760;780;800;820;840;860];  %Reservoir Temperature= 660 deg R (Literature)
u_uncorrected = ((1.709 * (10^(-5)-(2.062*10^(-6)*spgr))).*(T-460))+((8.118*10^(-3))-(6.15*10^(-3)*log10(spgr)));
yCO2 = 0.03;
yN2 = 0.02;
yH2S = 0.01;
u_CO2 = (yCO2*(((9.08*10^(-3))*(log10(spgr)))+ (6.24*10^(-3))));
u_N2 = (yN2*((8.48*10^(-3)*log10(spgr))+ (9.59*10^(-3))));
u_H2S = (yH2S*((8.49*10^(-3)*log10(spgr))+ (3.73*10^(-3))));
u1 = u_uncorrected + u_CO2 + u_N2 + u_H2S ;
Tpc = 168 + (325 * spgr) -(12.5*(spgr.^2)); 
Ppc = 677 + (15*spgr) -(37.5*(spgr.^2)); 
Tpr = T./Tpc;                 %CHANGED
Ppr = Pm./Ppc;                %CHANGED
% Constants for viscosity relation 
a0 = -2.4621182; 
a1 = 2.970547414;
a2 = -0.286264054; 
a3 = 0.008054205;
a4 = 2.80860949; 
a5 = -3.49803305;
a6 = 0.36037302; 
a7 = -0.01044324;
a8 = -0.793385648;
a9 = 1.39643306; 
a10 = -0.149144925; 
a11 = 0.004410155; 
a12 = 0.083938718; 
a13 = -0.186408848;
a14 =0.020336788; 
a15 = -0.000609579;
syms ug;
con = a0+(a1.*Ppr)+(a2.*(Ppr.^2))+ (a3.*(Ppr.^3)) +(Tpr.*(a4+(a5.*Ppr)+(a6.*Ppr.^2)+(a7.*Ppr.^3)))+((Tpr.^2).*(a8+(a9.*Ppr)+(a10.*Ppr.^2)+(a11.*Ppr.^3)))+((Tpr.^3).*(a12+(a13.*Ppr)+(a14.*Ppr.^2)+(a15.*Ppr.^3)));  %CHANGED IN TWO PLACES
eqn = ((Tpr.*ug) == u1.*exp(con));
temp = solve(eqn,'ug');
u_g = double(temp);
end

This will still not work, but it will get you to the much more compact

eqn =
 
 (5702507353183325*ug)/4503599627370496 == 7212478526205445/144115188075855872
    (2973544911973051*ug)/2251799813685248 == 433318337191181/9007199254740992
  (6238234906800469*ug)/4503599627370496 == 1518433413966557/36028797018963968
 (1613828264998639*ug)/1125899906842624 == 5989232554701665/144115188075855872
  (6523595956302411*ug)/4503599627370496 == 3031307013761477/72057594037927936
 (1667979088494805*ug)/1125899906842624 == 6063175485720917/144115188075855872
                          (1225*ug)/801 == 6021374973680469/144115188075855872
  (7178082536150291*ug)/4503599627370496 == 2979923091249657/72057594037927936
  (3658295761408275*ug)/2251799813685248 == 3003315655091799/72057594037927936
                         (49536*ug)/29683 == 754534745967413/18014398509481984
                         

This can be analyzed in a least-squared sense to get a best-fit ug of about 0.028997375328324588909163169559149