The supercritical water gasification (SCWG) of different kinds of feed including glycerol, lignin, humic acid, and ethylene glycol is investigated to predict product gas yields using a non-stoichiometric thermodynamic model. This model employs Gibbs free energy minimization, coupled with the penalty method as an optimization method. The results demonstrate excellent prediction accuracy for hydrogen yield, with average absolute relative deviations (AARDs) of 2.70%, 11.23%, and 0.17% for glycerol, humic acid, and ethylene glycol, respectively. Lignin prediction showed a higher AARD of 25.95%. Furthermore, the penalty method exhibited superior performance compared to the Lagrange method, achieving a reduction in error ranging from 66% to 88%. Moreover, the effect of reaction temperature and feed concentration on the molar gas yields was elucidated. This study establishes that the penalty method within the thermodynamic model effectively predicts product gas yields from biomass and bio-renewable feedstocks, with deviations below 10%. The developed thermodynamic model provides a reliable method for optimizing gasification processes, potentially improving the efficiency and accuracy of hydrogen production from diverse biomass and bio-renewable resources. This advancement supports the reduction in greenhouse gas emissions and promotes the use of sustainable energy sources.