A detailed description of an experimental setup based on the "static-analytic" technique with gas phase capillary sampling designed, built, and improved "in-house" to measure phase equilibria (pressure, temperature, and compositions) under gas hydrate formation conditions is presented in this work. The apparatus is suitable for measurements at temperatures ranging from 233 to 373 K and pressures up to 60 MPa. It was used to study phase equilibria in the carbon dioxide + methane + water system under hydrate formation conditions. An isochoric pressure-search method was used to measure hydrate dissociation conditions. The experimental data have been compared successfully with the literature data. The compositions of the gas phase in equilibrium with the hydrate and aqueous phases were measured using a gas chromatography technique and compared successfully with the literature data. The compositions of the hydrate and aqueous phases were determined by applying material balance equations. The experimental data on the compositions of the hydrate have been compared successfully with the literature data. To solve the latter equations, the Newton's numerical method coupled with the differential evolution optimization strategy was employed. All the aforementioned experimental data (hydrate dissociation conditions + composition analyses) have been compared with the predictions of two thermodynamic models, namely CSMGem and HWHYD. A discussion is made on the reliability of the predictions of the latter models.