Abundance-Weighted Carbon-Isotope Mixing in Natural Gas: Nonlinear Trajectories and Implications for Source Interpretation

Carbon isotope trends of light hydrocarbons in mature to overmature natural gases are commonly evaluated against gas wetness ([C2 + C3]/[C1 + C2 + C3]), yet the geometric effects of component-specific abundance contrasts are often conflated with reaction- or transport-driven fractionation. We develop an abundance-weighted framework for binary mixing that conserves 12C and 13C and relates the bulk mixing fraction x to a component-specific effective coordinate, ωi(x) = x/[x + (1 − x)ρi], where ρi is the abundance ratio of component i in the endmembers. Thus, δ13Ci is linear in ωi but generally nonlinear in x when ρi ≠ 1. Analytical expressions and C1–C3 benchmark simulations show that the “linear interpolation bias” is controlled jointly by isotopic contrast and abundance asymmetry, producing component-specific curvature of δ13Ci isotope vs. wetness trends. Binary mixing of fixed endmembers cannot produce a true rollover in an individual hydrocarbon isotope trajectory, although isotope-contrast metrics may develop local extrema because different components follow different effective mixing coordinates. Reparameterizing the trajectories by wetness can shift and nonlinearly compress or stretch pre-existing features along the horizontal axis, but it cannot create new extrema or change their amplitudes. The proposed framework therefore provides a mass-balance null model for evaluating mixing interpretations and identifying cases that require evolving endmembers, multistage charging, reaction, or transport fractionation.