Modelling Convective Dissolution of Carbon Dioxide and Finger Development with the Exponential Decay and Power Laws

Abstract Climate change is an emerging global crisis, largely due to the runaway emissions of carbon dioxide (CO₂) through the burning of fossil fuels. The inclusion of carbon capture and sequestration (CCS) into deep saline aquifers has become a promising mitigation strategy; however, the accurate simulation of CO₂ migration and dissolution continues to remain a challenge, owing to the complicated characteristics of subsurface reservoirs. This study expands existing modelling of CO₂ sequestration by integrating with fractional derivatives (involving power-law and exponential kernels) to encompass non-local and anomalous diffusion effects. In contrast to traditional methods, our model incorporates the factors of porous media heterogeneity, spatial variation of permeability, and complex CO₂-brine interaction into the simulation process, thus making it more physics-based in describing subsurface flow. This power-law behaviour is not captured in classical, exponential kernels, highlighting the importance of more sophisticated mathematical approaches when dealing with these types of processes, as demonstrated by numerical simulations. Our findings provide important insights into CO₂ plume dynamics, velocity fields, pressure distribution, injection behaviour, and the security of storage. Here, by evaluating flow stability and leakage risks, we show that permeability fluctuations modulate the efficiency of CO₂ dissolution and long-term containment. The approaches outlined in this paper enhance the confidence in CCS’s efficacy, whilst highlighting the importance of sound site selection, risk assessment, and regulatory regimes to support large volume deployment. This study combines theoretical modelling with practical implementation to provide a more predictable and flexible framework for CO₂ sequestration in heterogeneous geological formations. Ongoing research and innovative modelling will remain critical for delivering a viable pathway for large-scale climate mitigation amidst persisting economic and policy challenges.