Natural gases are complex, multicomponent mixtures for which most available theoretical approaches do not predict thermodynamic behavior correctly. Development of reliable and accurate models for these mixtures requires knowledge of the phase behavior for the component binaries over wide temperature and pressure ranges. This work provides an improved understanding of the properties of binary mixtures relevant to natural gases by reporting a systematic analysis of their phase behavior and classification within the van Konynenburg categories. We have used the molecular-based perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EOS) with conventional monoparametric Berthelot-Lorentz mixing rules to calculate and analyze the global phase diagrams of these binary systems and compared the results to experiments when possible. We have developed the PC-SAFT pure-compound and binary interaction parameters when necessary. We have studied the effects on the phase behavior of n-alkane configuration together with the behavior of other mixtures involving aromatics, carbon dioxide, nitrogen, and hydrogen sulfide. In this first study, we report the results for the binary systems n-alkane + n-alkane, whereas results for other binary systems appear in subsequent papers. Finally, we analyze the continuous transitions among the different patterns of fluid-phase behavior within homologous series. The binary systems studied demonstrate varied phase behavior, which PC-SAFT usually describes properly.