Upscaling of the constitutive relationships for CO2 migration in multimodal heterogeneous formations

Numerical modeling is a critical tool for site performance and risk assessment of geological stored CO2 at the reservoir scale. However, due to computational resource constraints, reservoir scale models have limitations in accounting for the details of the multi-scale heterogeneities. Appropriately averaged medium parameters are needed for the full scale modeling. In this study, we apply the macroscopic theory and present large-scale capillary pressure-relative permeability-saturation relationships that may be used as grid-block properties in the full-scale modeling. A macroscopic invasion percolation (MIP) model is developed, based on the assumption of capillary force dominance. Comparison of the MIP model with the numerical simulator TOUGH2/ECO2N for simulations of large-scale drainage capillary pressure curves shows a reasonably good match between results from the two models. Large-scale constitutive relationships are obtained through simulation procedures of CO2 displacing brine in multimodal heterogeneous media for ten cases with different geostatistical parameters. The large-scale constitutive relationships are mainly controlled by the proportion and the permeability variability of the background (framework) material, while the existence of the non-framework materials and their permeability variabilities may contribute, in a complex way, to the uncertainty in the large-scale constitutive relationships. In addition, the Leverett equation may well describe the relationship between the large-scale capillary pressure and absolute permeability when the sandstone (background material) proportion is high (>0.7). For cases with smaller sandstone proportions it may not be appropriate to link capillary pressure and absolute permeability through the Leverett equation. (C) 2012 Elsevier Ltd. All rights reserved.