In this research, an ANOVA analysis and a response surface methodology are applied to analyze the equilibrium of methanol reaction from pure carbon dioxide and hydrogen. In the ANOVA analysis, carbon monoxide composition in the feed, reaction temperature, recycle and water removal through a zeolite membrane are the analyzed factors. Carbon conversion, methanol yield, methanol productivity and methanol selectivity are the analyzed responses. Results show that main factors have the same effect on responses and a common significant interaction is not present. Carbon monoxide composition and water removal have a positive effect, while temperature and recycle have a negative effect on the system. From central composite design, an optimal solution is found in order to overcome thermodynamic limit: the reactor works with a membrane at lower temperature with carbon monoxide composition in the feed equal to 10 mol % and without recycle. In these conditions, carbon conversion, methanol yield, methanol selectivity, and methanol production are, respectively, higher than 60%, higher than 60%, between 90% and 95% and higher than 0.15 mol/h when considering a feed flow rate of 1 mol/h. A comparison with a traditional reactor is also developed: the membrane reactor ensures to have a carbon conversion higher of the 29% and a methanol yield higher of the 34%. Future researches should evaluate an economic analysis about the optimal solution.