Limits of Gas-Only Carbon-Budget Inference: Synthetic Gas–Water–Calcite Benchmarks for Quaternary Outgassing

Quaternary carbon-budget reconstructions combine gas observations with groundwater chemistry and dated carbonate deposits, which record different compartments and timescales. We examine the equilibrium partitioning step underlying such interpretations using an independent ideal-dilute calculation and 95 PHREEQC (pH–redox–equilibrium in C) cases in synthetic gas–water–calcite systems. At 25 ∘C, changing the headspace-to-water ratio from 0.01 to 10 L kg−1 changed the gas fraction of a 10 mmol carbon input in 1 kg water from 0.0118 to 0.9214. A strong-base-to-carbon ratio of one reduced the 1 L-headspace gas fraction from 0.5436 to 0.00892. At that ratio, increasing calcium availability could raise both mineral storage and residual gas expression. A non-limiting CO2 reservoir and a finite pressure-constrained bubble produced aqueous states indistinguishable at the reported precision under different carbon-budget constraints; the same finite inventory partitioned differently at fixed volume. Four selected phase classifications persisted across three databases. These results identify conditional limits of gas-only inventory inference, not corrections to published palaeofluxes. Application to dated travertines additionally requires water throughput, source attribution, preservation and chronology. The calculations provide reproducible equilibrium benchmarks and a framework for identifying missing constraints before phase-selective observations are combined into Quaternary carbon budgets.