Archives of Current Research International

Geological storage of CO₂ is an important approach for long-term climate change mitigation, but reliable prediction of subsurface plume behaviour requires mathematical models that clearly link physical assumptions to governing equations and numerical implementation. This study presents a derivation-only framework for a modified reaction–diffusion–advection model describing one-dimensional CO₂ concentration dynamics in a porous geological formation. Starting from mass conservation, the formulation incorporates pressure-driven advection, effective diffusion, linearised geochemical removal, injection input and caprock leakage in a single governing partial differential equation. The model is then expressed in dimensionless form to identify the Péclet number, Damköhler number and leakage number as controlling parameters for the relative influence of advective migration, diffusive spreading, geochemical trapping and containment loss. A DuFort–Frankel finite-difference discretisation is subsequently derived to obtain an explicit three-level update formula for numerical implementation. The resulting formulation provides a transparent theoretical basis for interpreting the roles of transport, reaction and leakage in simplified geological carbon storage systems. As the study does not include numerical experiments, benchmark comparison or field validation, the framework should be regarded as a foundation for future computational testing rather than a validated predictive tool.