Giant aquifers are capable of storing significant amounts of carbon as a result of immense water volumes, substantial dissolved inorganic carbon (DIC) concentrations and its ubiquitous reactions with matrix, thus contributing the global carbon storage and cycle. However, concentrations of dissolved solutes vary significantly over a distance in the Guarani Aquifer System (GAS) which causes difficulties in process interpretation. To quantify the importance of controlling parameters, we performed reactive transport modeling which combines both hydrological and geochemical inputs. The paper presents a chemical evolution in a two-dimensional aquifer configuration, global sensitivity analysis along with estimates of the DIC flux through the system boundaries. We observed that the DIC flux at recharge as well as plagioclase and olivine hydrolysis rates play an overriding importance in controlling the solute patterns including the DIC concentrations, while soil pH, horizontal hydraulic conductivity, porosity, precipitation of secondary minerals, but calcite, and Mg ratio in carbonates are of minor significance. If released Ca undergoes ion exchange to Na, the storage is delayed in time and space. In conclusion, the capacity of GAS in receiving recharge CO is attributed to the hydrolysis along with advective transport while the global sensitivity analysis informs how the financial resources should be allocated to effectively reduce interpretative uncertainty in large-scale groundwater systems.