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

Abstract

Summary 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 geocellular model. However, if no subgeocellular-scale information is included, 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 two-stage upscaling procedure for two-phase flow. In the first stage, we upscale from the core (fine) scale to the geocellular (intermediate) scale, while in the second stage we upscale from the geocellular 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. In contrast to most of the earlier investigations in this area, we first apply an iterative rate-dependent upscaling (iteration ensures that the properties are computed at the appropriate pressure gradient) rather than assume viscous or capillary dominance and, second, assess the accuracy of the two-stage upscaling procedure through comparison of flow results for the coarsened models against those of the finest-scale model. The two-stage method is applied to synthetic 2D reservoir models with strong variation in capillarity on the fine scale. 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. Introduction Because of computational costs, field-simulation models may have very coarse cells with sizes up to 100 to 200 m in horizontal directions. The cells are typically populated with effective properties (porosity, absolute permeability, relative permeabilities, and capillary pressure) upscaled from a geocellular (or geostatistical) model. In this way, the effects of heterogeneity on the geocellular scale will be included in the large-scale flow calculations. The cell sizes in geocellular models may be on the order of 20 to 50 m in horizontal directions. However, heterogeneities on much smaller scales (cm- to m- scale) may have a significant influence on the reservoir flow (Coll et al. 2001; Honarpour et al. 1994), and this potential effect cannot be captured if the upscaling starts at the geocellular scale.

Efficiency of a two-step upscaling method for permeability evaluation at Darcy and pore scales

“…Using a two-step upscaling approach reduced the computational costs and made it possible to perform a REV study. This kind of methods has also been used for two-phase flow in heterogeneous reservoirs [23,24].…”

Upscaling of the permeability by multiscale wavelet transformations and simulation of multiphase flows in heterogeneous porous media

“…In particular, a speedup factor of over 6,000 that we obtain for the Case 4 study in the presence of the capillary pressure is a demonstration of the method's high efficiency. Lohne et al [54] proposed a two-stage upscaling method for two-phase flows from core to simulation scale, arguing that heterogeneities in the sub-geological scales (centimeter to meter scale) may have a significant effect on flow in a reservoir which cannot be captured if the upscaling starts at the geostatistical scale. They computed the effective properties for the geological units at the geostatistical scale by starting the upscaling at a small scale.…”

Large-scale Invasion Percolation with Trapping for Upscaling Capillary-Controlled Darcy-scale Flow

“…Nevertheless, it is usually observed that at relatively small scales capillary forces dominate the displacement process, while viscous and gravitational forces may become more important at larger scales (Odsaeter et al 2015;Kumar and Jerauld 1996;Jonoud and Jackson 2008a). Numerous upscaling methods are available in the literature for two-phase flow (Guzman et al 1999;Jacks et al 1973;Kyte and Berry 1975;Stone 1991;Pickup and Sorbie 1996;Lohne et al 2006;Virnovsky et al 2004;King 1989;King et al 1993;Coll et al 2001;Wallstrom et al 2002;Durlofsky 1997) among which flow-based methods are considered the most reliable. Under this category, two fundamental approaches are employed: steady-state and dynamic pseudos.…”