Upscaling of CO₂ injection into brine with capillary heterogeneity effects

The large-scale simulation of CO₂ storage operations can be expensive computationally, particularly when the effects of fine-scale capillary pressure heterogeneity are included. The application of upscaling techniques could lead to substantial reductions in computational cost. This work targets the development of an upscaling procedure that is applicable for the CO₂ injection stage, which corresponds to a drainage process. Specifically, we develop and apply a new upscaling technique for two-phase flow in heterogeneous formations with capillary heterogeneity effects. The procedure entails first upscaling capillary pressure in the capillary limit, and then computing coarse-scale relative permeability functions using a global dynamic upscaling procedure. An iterative method is applied to enhance the accuracy of the upscaled capillary pressure functions. The new dynamic upscaling approach is applied to a synthetic heterogeneous two-dimensional aquifer model that involves injection of CO₂ into brine. Fine-scale simulation results are compared with coarse-scale results generated using both the dynamic upscaling approach and a simpler method that entails the use of upscaled capillary pressure in conjunction with rock relative permeability curves. It is shown that the dynamic upscaling procedure provides results that are close to those from the fine-scale simulation and are consistently more accurate than results from the simpler method. The upscaling procedure is tested over a range of injection rates spanning three orders of magnitude. We show that, although the upscaled functions are in general rate dependent, accurate coarse-scale results can be obtained using upscaled relative permeability functions computed at only two different flow rates. We also observe that the model constructed using our method retains reasonable accuracy even when the flow problem differs from that used to compute the upscaled functions.