Including Fine-Scale Capillary Heterogeneity in Modeling the Flow of CO2 and Brine in Reservoir Cores

Advisors

Sally M. Benson
Hamdi Tchelepi

Abstract

Experimental evidence by several groups, including ours, indicates that spatial variations in the capillary-pressure-saturation relationship can dominate the distribution and transport dynamics CO₂-brine systems in natural porous media. The importance of such small-scale capillary heterogeneity depends strongly on the local balance between the viscous, buoyancy, and capillary forces. Our objective is to develop a rigorous mathematical and numerical framework that models the physics of CO₂-brine systems with high fidelity, which can then be used to study the behavior of large-scale systems of practical interest.

The Stanford General-Purpose Research Simulator (GPRS) is used in this study. The simulator was modified to account for capillary heterogeneity. The locally conservative finite-volume scheme employs pressure and saturation as primary variables. Significant differences in the capillary pressure functions among neighboring grid blocks lead to discontinuities in the saturation distribution across grid block boundaries. Such discontinuities can pose serious problems in numerical models. Here, we show the 'standard' (first-order in space and time) Fully Implicit Method (FIM) with single-point phase-based upwinding resolves the saturation field correctly for both continuous and discontinuous capillary pressure conditions. We also show that in the cases when the capillary pressure is physically undefined due to the absence of a second fluid phase, in order for the simulator to obtain the potential directions of the physically connected phase, a value should be assigned to the capillary pressure, as if an infinitesimal amount of the absent phase is present. Such approach will not cause unphysical flow when single-point phase-based upstream weighting is used.

We demonstrate our ability to model the immiscible two-phase flow processes in the presence of strong spatial heterogeneity in both the permeability and capillary-pressure relations. Results are analyzed using existing semi-analytical solutions and experimental observations. Finally, the simulation of a CO₂ core flooding experiment was performed. The results are in good agreement with the high-resolution Computerized Tomography measurements. Comparisons between GPRS and TOUGH2-MP indicate a good agreement, but GPRS outperforms TOUGH2-MP in terms of computational speed.