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The study of the technology of flame enrichment with oxygen, together with the study of soot formation coupled with thermal radiation, has attracted interest in industries that involve combustion processes where a large amount of energy is released as heat and, consequently, light. The main objective of combustion is maximize the heat while minimizing the production of polluting gases. The more harmonic the union of these elements, the more efficient the combustion will be. The stoichiometry of the fuel composition provides a basis to calculate the required amount to be burnt in the reaction. Although there are existing studies on the mechanisms of soot formation and control, a more detailed understanding of these processes is important for technological advances in environmental impact (emission of polluting gases). In this study, we investigate the self-affinity of time series of thermal radiation from two fuels, natural gas (NG) and acetylene (AC), enriched with oxygen at 21\%, 23\% and 25\% concentrations during the combustion process. We used the detrended fluctuation analysis method to evaluate the burning process of these fuels. We found a well-defined self-affine aspect for these gases in this dynamic process. Using the proposed method, we were able to characterize the time series of NG as a sub-diffusive process and the time series of AC as a process with persistent self-affinity.