This paper made an effort to establish a thermodynamic fundamental for evaluating the energy quality that is a basis of state evaluation and process analysis to effectively use fossil fuels. On base of the thermodynamic consistency, the energy quality factor was defined as an index for the energy quality of a fluid. General methods of calculating the enthalpy and the energy quality factor of fluid were established by means of defining standard enthalpy. The standard exergy, the standard enthalpy, and the standard energy quality factor of common pure species related to combustion of fossil fuels were given. A graphic methodology on the energy factor and related functions, enthalpy and exergy, was proposed for investigating the state characteristics and process performance. To validate and demonstrate the approaches, four routes of methane combustion have been investigated in the a-H-E diagram. The results show that preheating and endothermic reforming before combustion can result in the cascade utilization of methane, which appears as a gradual decrease in the energy quality factor. The results prove that the exergy regeneration through conversions of heat and substance is important for the effective use of fossil fuels.