A multi-scale and multi-mechanism coupled model for carbon isotope fractionation of methane during shale gas production

Prediction of production decline and evaluation of the adsorbed/free gas ratio are critical for determining the lifespan and production status of shale gas wells. Traditional production prediction methods have some shortcomings because of the low permeability and tightness of shale, complex gas flow behavior of multi-scale gas transport regions and multiple gas transport mechanism superpositions, and complex and variable production regimes of shale gas wells. Recent research has demonstrated the existence of a multi-stage isotope fractionation phenomenon during shale gas production, with the fractionation characteristics of each stage associated with the pore structure, gas in place (GIP), adsorption/desorption, and gas production process. This study presents a new approach for estimating shale gas well production and evaluating the adsorbed/free gas ratio throughout production using isotope fractionation techniques. A reservoir-scale carbon isotope fractionation (CIF) model applicable to the production process of shale gas wells was developed for the first time in this research. In contrast to the traditional model, this model improves production prediction accuracy by simultaneously fitting the gas production rate and δ¹³C₁ data and provides a new evaluation method of the adsorbed/free gas ratio during shale gas production. The results indicate that the diffusion and adsorption/desorption properties of rock, bottom-hole flowing pressure (BHP) of gas well, and multi-scale gas transport regions of the reservoir all affect isotope fractionation, with the diffusion and adsorption/desorption parameters of rock having the greatest effect on isotope fractionation being D∗/D, P_L, V_L, α, and others in that order. We effectively tested the universality of the four-stage isotope fractionation feature and revealed a unique isotope fractionation mechanism caused by the superimposed coupling of multi-scale gas transport regions during shale gas well production. Finally, we applied the established CIF model to a shale gas well in the Sichuan Basin, China, and calculated the estimated ultimate recovery (EUR) of the well to be 3.33 × 10⁸ m³; the adsorbed gas ratio during shale gas production was 1.65%, 10.03%, and 23.44% in the first, fifth, and tenth years, respectively. The findings are significant for understanding the isotope fractionation mechanism during natural gas transport in complex systems and for formulating and optimizing unconventional natural gas development strategies.