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"abstract": "Based on\u00a0quantum chemistry\u00a0calculations for normal octane homolytic cracking, a kinetic\u00a0hydrogen isotope\u00a0fractionation model for methane, ethane, and\u00a0propane\u00a0formation is proposed. The activation energy differences between D-substitute and non-substituted methane, ethane, and propane are 318.6, 281.7, and 280.2\u00a0cal/mol, respectively. In order to determine the effect of the entropy contribution for hydrogen isotopic substitution, a transition state for ethane bond rupture was determined based on density function theory (DFT) calculations. The kinetic\u00a0isotope effect\u00a0(KIE) associated with bond rupture in D and H substituted ethane results in a frequency factor ratio of 1.07. Based on the proposed\u00a0mathematical model\u00a0of hydrogen isotope fractionation, one can potentially quantify natural gas\u00a0thermal maturity\u00a0from measured hydrogen isotope values. Calculated gas maturity values determined by the proposed mathematical model using \u03b4D values in ethane from several basins in the world are in close agreement with similar predictions based on the \u03b413C composition of ethane. However, gas maturity values calculated from field data of methane and propane using both hydrogen and carbon kinetic isotopic models do not agree as closely. It is possible that \u03b4D values in methane may be affected by microbial mixing and that propane values might be more susceptible to hydrogen exchange with water or to analytical errors. Although the model used in this study is quite preliminary, the results demonstrate that kinetic isotope fractionation effects in hydrogen may be useful in quantitative models of natural gas generation, and that \u03b4D values in ethane might be more suitable for modeling than comparable values in methane and propane.",
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