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Abstract We present a multi-point flux approximation (MPFA) scheme for simulation of 3-D multi-phase flow on adapted grids. It is an extension of the VCMP (Variable Compact Multi-Point) scheme, which constructs stencils that are locally adapted to flow through transmissibility upscaling. The proposed integration of upscaling, MPFA stencil selection and gridding leads to an optimized flow discretization that can accurately resolve full-tensor effects, is compact, and leads to low upscaling errors. The grid adaptivity is driven by both upscaling, in a pre-processing stage, and by solution gradients during run-time. During transmissibility upscaling, the grid is refined to resolve important flow features such as high permeability flow paths. During run-time, we refine the grid locally, as needed, to accurately resolve saturation fronts, and coarsen once the front passes. We do not employ downscaling techniques, but compute transmissibilities for the newly refined regions using the upscaling methodology that can be effectively applied to localized regions. The numerical tests presented in this paper show that the method leads to higher upscaling accuracy as compared to commonly used upscaling methods. On average, error in total flow is reduced by a factor of two, and the fine-scale velocity field is resolved with greater accuracy as well. They also illustrate that saturation fronts can be resolved accurately using single-phase upscaling only by employing VCMP on adapted grids. The combined strategy promises to significantly improve the workflow of coarse-scale modeling for flow simulations such as those routinely performed in the industry. Introduction Subsurface formations may exhibit geometrically complex geological features that must be well represented in simulations of flow and transport because they can fundamentally impact simulation results. However, to reduce computational costs, simulations are generally performed on grids that are coarse compared to the given geocellular grids. A typical geocellular model of a heterogeneous subsurface formation is composed of 10 - 10 cells. It is generally upscaled by a factor of 10 to 1000 in practical reservoir simulation settings. The resulting coarse scale simulation models should retain the key features of the geology and the flow. Permeability or grid nonorthogonality effects can introduce full-tensor effects, which complicate the process of finding accurate upscaled models. It is generally accepted that multi-point flux approximations (MPFA) are required to accurately represent such full-tensor effects in finite-volume based flow models. These methods express the flux between two adjacent grid blocks not only in terms of the pressure in those grid blocks, as in two-point flux approximations (TPFA), but also in terms of pressures in a number of other grid blocks near the face.
- North America > United States (0.46)
- Europe > Norway > Norwegian Sea (0.24)
Abstract Upscaling is often applied to generate practical simulation models from highly detailed geocellular descriptions. In this paper we develop and evaluate a new upscaling procedure - a variable compact multipoint adaptive local-global technique (VCMP-ALG) - that is able to capture, accurately and efficiently, both full-tensor and global flow effects in the coarse model. The method successfully combines the positive attributes of its two underlying component procedures: the variable compact multipoint (VCMP) flux scheme, which provides coarse-scale transmissibilities that are appropriate for use in problems characterized by strong full-tensor permeabilities, and adaptive local-global (ALG) upscaling, which accounts for the effects of large-scale flow in the upscaling computations without solving any global fine-scale flow problems. The performance of the local-global CMP upscaling technique is evaluated for multiple realizations of oriented variogram-based models and synthetic deltaic systems. Extensive numerical results for 2D cases demonstrate that the VCMP-ALG approach provides better overall accuracy than either of the underlying methods - an extended local VCMP technique and an adaptive local-global procedure based on two-point flux approximations - applied individiually. The extension of the VCMP-ALG method to irregular quadrilateral grids is also accomplished. Finally, we present results for two-phase oil-water flows, for which the models based on the VCMP-ALG method again provide the best overall accuracy. Introduction Fine-scale geological descriptions are often too detailed to be used directly for flow simulation. For this reason some type of upscaling is often required. A key quantify computed in the upscaling procedure is the coarse-scale permeability or transmissibility. A wide variety of permeability and transmissibility upscaling methods have been presented in the literature (see e.g., Durkofsky, 2005; Farmer, 2002; Gerritsen and Durlofsky, 2005, for recent reviews). These techniques can be viewed in terms of the size of the domain used to calculate the coarse-scale parameters. Options include local methods (e.g., Durlofsky, 1991; King and Mansfield, 1999), in which the upscaled parameters are computed using only the fine-scale permeabilities corresponding to the target coarse block; extended local methods (e.g., Wen et al., 2003a,b; Wu et al., 2002), where a border region around the target coarse block is introduced; and global methods (Chen et al., 2008; Holden and Nielsen, 2000; Mallison et al., 2006; Zhang et al., 2008), in which a global flow solution is used to compute the upscaled properties. Other useful methods are so-called quasi-global techniques (e.g., Chen and Durkofsky, 2006; Chen et al., 2003; Gerritsen and Lambers, 2008; Wen et al., 2006), where approximate global information (rather than fine-scale flow solutions) is used for the upscaling. Our goal in this work is to develop accurate quasi-global upscaling techniques that are suitable for use in systems exhibiting significant full-tensor permeability effects.
- Europe (0.93)
- North America > United States (0.46)