## 4 Discussion
### Relations between Parameters
#### 4.1.3 Carbon Isotope Ratios (\(\delta^{13}\)C\({}_{\text{CO2}}\))  
Another way to infer the origin of the CO\({}_{2}\) gas phase is to refer to carbon-13 isotope-ratio determinations (Figure 6). As shown during the baseline site characterization, carbon-isotope ratios mainly fall within a range of \(-19\) to \(-28\%\) VPDB. A larger range was established by [PERSON] [70] (\(-15\) to \(-25\%\)). The \(-19\) to \(-28\%\) range is the result of CO\({}_{2}\) isotope equilibration with that of biological organisms in the soil under steady-state conditions [71] and more specifically the equilibration with vegetation whose photosynthetic cycle produces molecules with three carbon atoms (Calvin cycle). Molecules produced under the Calvin cycle have carbon-isotope ratios ranging from \(-21\) to \(-33\%\)[72] with a mean value of \(-27\%\) VPDB. The CO\({}_{2}\) produced from these molecules is enriched by a factor close to \(+4.4\%\)[73], leading to \(\delta^{13}\)C\({}_{\text{CO2}}\) ranging from \(-17\) to \(-29\%\), the most common values in a temperate climate being near \(-22\) to \(-25\%\)[74] with possible extension to more depleted ratios (down to \(-28\%\); [75]) or to more enriched ratios (up to \(-13\%_{0}\); [76]). Applied to our dataset, this suggests that the presence of CO\({}_{2}\) in soil over the Lacq-Rousse storage site is essentially the result of natural biological processes occurring in soil. If the CO\({}_{2}\) were produced from the remaining CH\({}_{4}\) in the storage reservoir, it should have a lower \(\delta^{13}\)C\({}_{\rm CO2}\), as equilibration with CH\({}_{4}\) having a lower \(\delta^{13}\)C\({}_{\rm CH4}\) (\(\delta^{13}\)C\({}_{\rm CH4}\) of the Lacq-Rousse field: \(-41\) to \(-43\%\) VPDB; [67]) will produce depleted \(\delta^{13}\)C\({}_{\rm CO2}\)[75]. Similarly, the injected CO\({}_{2}\), produced by CH\({}_{4}\) oxy-combustion, has a \(\delta^{13}\)C\({}_{\rm CO2}\) of \(-40\%\)[67]. Although some re-equilibration and/or dissolution processes in water may occur in a 4500-m-thick sedimentary pile, it is very unlikely that the monitored carbon-isotope ratios of the CO\({}_{2}\) originate from the storage reservoir. A difference larger than \(10\%\) between injected CO\({}_{2}\) and baseline CO\({}_{2}\) is recognized as representing favorable conditions for the use of carbon isotope ratios as a tracer [77]. The hypothesis of CO\({}_{2}\) originated from the reservoir is tested in Figure 6B for the five samples having ratios lower than \(-28\%\). The isotope composition of the CO\({}_{2}\) that may originate from the storage is taken at \(-40\%\) and mixing with soil gas is calculated (using the \(-15\%\) and \(-28\%\) endmembers). Three samples are outside binary mixing relations - to plot under such relations, the soil gas component should have a ratio more depleted than \(-28\%\)--founding such a depleted ratio in soil is very unlikely. Only two samples may plot on a binary relation between CO\({}_{2}\) from the storage and CO\({}_{2}\) from the soil (at \(-23\%\)) but this is not in agreement with other data. Analyses of noble gases in soil gas highlight the presence of atmospheric endmembers (neither \({}^{4}\)He nor \({}^{84}\)Kr enrichment), whereas the gas phase from the reservoir has a very different noble-gas signature [70]. Nevertheless, some \(\delta^{13}\)C\({}_{\rm CO2}\) ranging from \(-18\%\) to \(-11\%\) VPDB are not explained--or are partly explained--by the previous statements; they are less depleted in the heavy isotope (\({}^{13}\)C) than the majority of the data. Such deviations may be attributed to contamination by atmospheric CO\({}_{2}\) (\(\delta^{13}\)C\({}_{\rm CO2}\) of \(-8.4\%\); [78]) at least for data that plot close to the dilution lines reported in Figure 6A and that have low CO\({}_{2}\) concentrations (<0.2% vol. i.e., 1/CO\({}_{2}\) >5).