COMPLEX CHEMICAL EQUILIBRIUM BY GIBBS ENERGY MINIMIZATION 4.(b2)  |POLVER05_3 |2
f(lamda1) = 2 * CO2 + CO + 2 * O2 + H2O - 4 # Oxygen balance
f(lamda2) = 4 * CH4 + 4 * C2H4 + 2 * C2H2 + 2 * H2 + 2 * H2O + 6 * C2H6 - 14 # Hydrogen balance
f(lamda3) = CH4 + 2 * C2H4 + 2 * C2H2 + CO2 + CO + 2 * C2H6 - 2 # Carbon balance
f(H2) = ln(H2 / sum) + 2 * lamda2
f(H2O) = -46.03 / R + ln(H2O / sum) + lamda1 + 2 * lamda2
f(CO) = -47.942 / R + ln(CO / sum) + lamda1 + lamda3
f(CO2) = -94.61 / R + ln(CO2 / sum) + 2 * lamda1 + lamda3
f(CH4) = 4.61 / R + ln(CH4 / sum) + 4 * lamda2 + lamda3
f(C2H6) = 26.13 / R + ln(C2H6 / sum) + 6 * lamda2 + 2 * lamda3
f(C2H4) = 28.249 / R + ln(C2H4 / sum) + 4 * lamda2 + 2 * lamda3
f(C2H2) = C2H2 - exp(-(40.604 / R + 2 * lamda2 + 2 * lamda3)) * sum
f(O2) = O2 - exp(-2 * lamda1) * sum
R = 1.9872
sum = H2 + O2 + H2O + CO + CO2 + CH4 + C2H6 + C2H4 + C2H2
# Calculation of the objective function
G_O2 = O2 * ln(abs(O2 / sum))
G_H2 = H2 * ln(H2 / sum)
G_H2O = H2O * (-46.03 / R + ln(H2O / sum))
G_CO = CO * (-47.942 / R + ln(CO / sum))
G_CO2 = CO2 * (-94.61 / R + ln(CO2 / sum))
G_CH4 = CH4 * (4.61 / R + ln(abs(CH4 / sum)))
G_C2H6 = C2H6 * (26.13 / R + ln(abs(C2H6 / sum)))
G_C2H4 = C2H4 * (28.249 / R + ln(abs(C2H4 / sum)))
G_C2H2 = C2H2 * (40.604 / R + ln(abs(C2H2 / sum)))
ObjFun = G_H2 + G_H2O + G_CO + G_O2 + G_CO2 + G_CH4 + G_C2H6 + G_C2H4 + G_C2H2
H2(0) = 5.992
O2(0) = 0.0001 > 0
H2O(0) = 1
CO(0) = 1
CH4(0) = 0.001 > 0
C2H4(0) = 0.001 > 0
C2H2(0) = 0.001 > 0
CO2(0) = 0.993
C2H6(0) = 0.001 > 0
lamda1(0) = 10
lamda2(0) = 10
lamda3(0) = 10