Gas hydrates are crystalline structures formed by water molecules and compounds of low molecular weights, being formed under suitable conditions of pressure and temperature. Although initially considered as inconveniences to the natural gas industries, they are currently considered as promising alternatives for solving some important global issues, such as contributing to the reduction of effects caused by the greenhouse gases. This concern related to the control of emissions of polluting gases has mobilized hundreds of countries that, at the United Nations Climate Change Conference (COP), agreed to reduce emissions of carbon dioxide and other gases by 2100. However, despite several strategies in the reduction of carbon dioxide emissions have been proposed, many rely on political incentives and substantial investments to convert pre-existing technologies to clean technologies, making such applicability and adaptability problematic. Thus, innovative Carbon Capture and Storage (CCS) techniques are being studied, which considers the use of gas hydrates formation to trap these gases, presents perspectives of lower costs and low environmental damages, promising to overcome the above mentioned problem, besides capturing and storing adequately the carbon dioxide and methane emitted. The need for robust evaluation of the thermodynamic equilibrium of hydrate-containing systems arises in order to make the proposal feasible and used on a large scale. The present work extensively solidifies this assessment of hydrate phase equilibria by proposing the isofugacity and Gibbs energy minimization criteria coupled to the nonlinear programming for the calculation of phase equilibria in the formation of methane and carbon dioxide hydrates. The Soave-Redlich-Kong cubic equation (SRK) was used to calculate the liquid and gaseous phases, and the Van der Waals and Platteeuw models were used to describe the solid phase of the hydrate. The procedure was implemented in the General Algebraic Modeling System (GAMS) software and in the CONOPT3 solver, with some numerical procedures performed in Microsoft Office Excel. The comparison between the results obtained from the present study by the isofugacity criterion and experimental data has been carried out, allowing concluding the satisfactory prediction of the phase equilibria behavior of systems containing hydrates.