Mathematical modeling of stable carbon isotope ratios in natural gases

A new approach is presented for mathematical modeling of stable carbon isotope ratios in hydrocarbon gases based on both theoretical and experimental data. The kinetic model uses a set of parallel first-order gas generation reactions in which the relative cracking rates of isotopically substituted (k*) and unsubstituted (k) bonds are represented by the equation k*/k = (A(f)*/A(f)) exp(-Delta Ea/RT), where R is the gas constant and T is temperature. Quantum chemistry calculations have been used to estimate the entropic (A(f)*/A(f)) and enthalpic (Delta Ea) terms for homolytic bond cleavage in a variety of simple molecules. For loss of a methyl group from a short-chain n-alkane (less than or equal to C6), for example, we obtain an average Delta Ea of 42.0 cal/mol and an average A(f)*/A(f) of 1.021. Expressed differently, C-13-methane generation is predicted to be 2.4% (24 parts per thousand) slower than C-12-methane generation (from a short-chain n-alkane) in a sedimentary basin at 200 degrees C butonly 0.7% (7 parts per thousand) slower in a laboratory heating experiment at 500 degrees C. Similar calculations carried out for homolytic bond cleavage in other molecules show that with few exceptions, Delta Ea varies between 0 and 60 cal/mol and A(f)*/A(f) between 1.00 and 1.04. Examination of this larger data set reveals: (1) a weak sigmoid relationship between Delta Ea and bond dissociation energy; and (2) a strong positive correlation between Delta Ea and A(f)*/A(f). The significance of these findings is illustrated by fitting a kinetic model to chemical and isotopic data for the generation of methane from n-octadecane under isothermal closed-system conditions. For a specific temperature history, the fitted model provides quantitative relationships among methane carbon isotope composition, total methane yield and methane generation rate which may have relevance to the cracking of oil-prone kerogens and crude oil. The observed variability of the kinetic reactivity of various methane source rocks highlights the need to apply and adequately calibrate such models with laboratory data for specific study areas. With this approach isotope data of natural gases can be used not only to estimate the time of gas generation in a sedimentary basin, but also to evaluate the source rock maturities at which specific accumulations were generated, and place constraints on trap charging histories. Copyright (C) 2000 Elsevier Science Ltd.