Evaluating numerical simulation errors of CO₂-brine flow with capillary heterogeneity using a 1D semi-analytical solution

Modeling CO₂-brine flow related to CO₂ storage in saline aquifers involves intense numerical simulations. One of the important processes associated with these flows, allowing for safe long term storage of CO₂, is residual trapping. For accurate modeling of trapping, capillary heterogeneity should be incorporated in the models. However, there have been some reports of increased numerical simulation errors associated with these models and yet no systematic study of their accuracy has been carried out. We compare results of two numerical simulators to a semi-analytical solution of 1D two-phase immiscible steady state flow with capillary heterogeneity. Simulation errors are calculated for a wide range of different flow rates, fluid fractions, capillary pressure curves and heterogeneities. Results show that capillary pressure and saturation errors increase with smaller dimensionless capillary number and reach large values of 25−50% for many cases. It is shown that the errors are related to capillary heterogeneity and therefore increase also with larger variance of log permeability. Finally, a new approach for predicting numerical errors without employing an analytical solution is proposed, i.e., the error indicator analysis.