We review and perform comparison studies for three recent multiscale methods for solving elliptic problems in porous media flow; the multiscale mixed finite-element method, the numerical subgrid upscaling method, and the multiscale finite-volume method. These methods are based on a hierarchical strategy, where the global flow equations are solved on a coarsened mesh only. However, for each method, the discrete formulation of the partial differential equations on the coarse mesh is designed in a particular fashion to account for the impact of heterogeneous subgrid structures of the porous medium. The three multiscale methods produce solutions that are mass conservative on the underlying fine mesh. The methods may therefore be viewed as efficient, approximate fine-scale solvers, i.e., as an inexpensive alternative to solving the elliptic problem on the fine mesh. In addition, the methods may be utilized as an alternative to upscaling, as they generate mass-conservative solutions on the coarse mesh. We therefore choose to also compare the multiscale methods with a state-of-the-art upscaling method -the adaptive local-global upscaling method, which may be viewed as a multiscale method when coupled with a mass-conservative downscaling procedure. We investigate the properties of all four methods through a series of numerical experiments designed to reveal differences with regard to accuracy and robustness. The numerical experiments reveal particular problems with some of the methods, and these will be discussed in detail along with possible solutions. Next, we comment on implementational aspects and perform a simple analysis and comparison of the computational costs associated with each of the methods. Finally, we apply the three multiscale methods to a dynamic twophase flow case and demonstrate that high efficiency and accurate results can be obtained when the subgrid computations are made part of a preprocessing step and not updated, or updated infrequently, throughout the simulation.

No abstract

No abstract

Polymer injection for viscous oil displacement has proven effective and gained interest in the recent years. The two general types of EOR polymers available for field applications, synthetic and biological, display different rheological properties during flow in porous media. In this paper, the impact of rheology on viscous oil displacement efficiency and front stability is investigated in laboratory flow experiments monitored by X-ray. Displacement experiments of crude oil (~500cP) were performed on large Bentheimer rock slab samples (30×30cm) by secondary injection of viscous solutions with different rheological properties. Specifically, stabilization of the aqueous front by Newtonian (glycerol and shear degraded HPAM) relative to shear thinning (Xanthan) and shear thickening (HPAM) fluids was investigated. An X-ray scanner monitored the displacement processes, providing 2D information about fluid saturations and distributions. The experiments followed near identical procedures and conditions in terms of rock properties, fluxes, pressure gradients, oil viscosity and wettability. Secondary mode injections of HPAM, shear-degraded HPAM, xanthan and glycerol solutions showed significant differences in displacement stability and recovery efficiency. It should be noted that concentrations of the chemicals were adjusted to yield comparable viscosity at a typical average flood velocity and shear rate. The viscoelastic HPAM injection provided the most stable and efficient displacement of the viscous crude oil. However, when the viscoelastic shear-thickening properties were reduced by pre-shearing the polymer, the displacement was more unstable and comparable to the behavior of the Newtonian glycerol solution. Contrary to the synthetic HPAM, xanthan exhibits shear thinning behavior in porous media. Displacement by xanthan solution showed pronounced viscous fingering with a correspondingly early water breakthrough. These findings show that at adverse mobility ratio, rheological properties in terms of flux dependent viscosity lead to significant differences in stabilization of displacement fronts. Different effective viscosities should arise from the flux contrasts in an unstable front. The observed favorable "viscoelastic effect", i.e. highest efficiency for the viscoelastic HPAM solution, is not linked to reduction in the local Sor. We rather propose that it stems from increased effective fluid viscosity, i.e. shear thickening, in the high flux paths. This study demonstrates that rheological properties, i.e. shear thinning, shear thickening and Newtonian behavior largely impact front stability at adverse mobility ratio in laboratory scale experiments. Shear thickening fluids were shown to stabilize fronts more effectively than the other fluids. X-ray visualization provides an understanding of oil recovery at these conditions revealing information not obtained by pressure or production data.