Two-Stage Upscaling of Two-Phase Flow: From Core to Simulation Scale

Abstract

Abstract In the coarse scale simulation of heterogeneous reservoirs, effective or upscaled flow functions, e.g., oil and water relative permeability and capillary pressure, can be used to represent heterogeneities at subgrid scales. The effective relative permeability is typically upscaled along with absolute permeability from a geostatistical model. However, the potentially important effects of smaller scale heterogeneities (on the centimeter to meter scale) in both capillarity and absolute permeability will not be captured by this approach. In this paper, we present a new two-stage upscaling procedure for two-phase flow. In the first stage, we upscale from the core (fine) scale to the geostatistical (intermediate) scale, while in the second stage we upscale from the geostatistical scale to the simulation (coarse) scale. The computational procedure includes numerical solution of the finite difference equations describing steady state flow over the local region to be upscaled, using either constant pressure or periodic boundary conditions. The two-stage method is applied to synthetic two-dimensional reservoir models with strong variation in capillarity on the fine scale. Results are presented in terms of both oil production rates and saturation fields. Accurate reproduction of the fine grid solutions (simulated on 500 × 500 grids) is achieved on coarse grids of 10 × 10 for different flow scenarios. It is shown that, although capillary forces are important on the fine scale, the assumption of capillary dominance in the first stage of upscaling is not always appropriate, and that the computation of rate dependent effective properties in the upscaling can significantly improve the accuracy of the coarse scale model. The assumption of viscous dominance in the second upscaling stage is found to be appropriate in all of the cases considered.