Graph theory based estimation of probable CO2 plume spreading in siliciclastic reservoirs with lithological heterogeneity

Estimating plume spreading in geological CO₂ storage reservoirs is critical for several reasons including the assessment of pore space utilization efficiency, preferential CO₂ migration pathways and trapping. However, plume spreading critically depends on lithological heterogeneity of the reservoir and CO₂ injection rate. It might require numerous high fidelity full physics numerical simulations to constrain the uncertainty in plume spreading for a given reservoir. This might not always be practical due to computational limitations. Hence, reduced physics approaches, such as invasion-percolation method and machine learning, could be useful to answer certain questions on plume spreading in the subsurface. This study presents a new reduced physics approach based on graph theory for estimating probable CO₂ plume migration under very low and very high injection rates. The two end-member scenarios are assessed by performing random walk in the 3D reservoir space to constrain 20,000 possible paths of CO₂ flow away from the injection well. The resistance to CO₂ flow associated with each path is computed for viscous, capillary and gravity forces. The resistances are then transformed into the likelihood of CO₂ migration along the path. The algorithm was applied to 45 reservoir models with varying degrees of lithological heterogeneity and the results were compared to those from full physics and invasion percolation simulations. The graph theory results showed a close match with the results from full physics approach for both flow regimes and with results from invasion-percolation approach for capillary-gravity dominated flow regime. The algorithm was further applied to answer key questions on reservoir screening such as pore space utilization potential. The graph theory approach was also integrated with machine learning to predict CO₂ saturation. Testing suggested that the graph theory approach can be as much as 50 and 20 times faster than the full physics numerical simulations and invasion-percolation simulations, respectively.