Effect of Grid Deviation on Flow Solutions

Abstract

The two-point flux finite-volume method (2P-FVM) is the most widely used method for solving the flow equation in reservoir simulations. For 2P-FVM to be consistent, the simulation grid needs to be orthogonal (or k-orthogonal if the permeability field is anisotropic). It is well known that corner-point grids can introduce large errors in the flow solutions because of the lack of orthogonality in general. Multipoint flux formulations that do not rely on grid orthogonality have been proposed, but these methods add significant computational cost to solving the flow equation.Recently, 2.5D unstructured grids that combine 2D Voronoi areal grids with vertical projections along deviated coordinate lines have become an attractive alternative to corner-point gridding. The Voronoi grid helps maintain orthogonality areally and can mitigate grid orientation effects. However, experience with these grids is limited.In this paper, we present an analytical and numerical study of these 2.5D unstructured grids. We focus on the effect of grid deviation on flow solutions in homogeneous, but anisotropic, permeability fields. In particular, we consider the grid deviation that results from gridding to sloping faults. We show that 2P-FVM does not converge to the correct solution as the grid refines. We further quantify the errors for some simple flow scenarios using a technique that combines numerical analysis and asymptotic expansions. Analytical error estimates are obtained. We find that the errors are highly flow dependent and that they can be global with no strong correlation with local nonorthogonality measures. Numerical tests are presented to confirm the analytical findings and to show the applicability of our conclusions to more-general flow scenarios.

Generation and application of adaptive PEBI grid for numerical well testing(NWT)

“…Around the border, PEBI grids lose the feature of orthogonality to radial grids. This would cause unnecessary numerical errors [9]. Our method can avoid these flaws and make better grids.…”

Accurate Modeling of Faults by Multipoint, Mimetic, and Mixed Methods

“…Such a gridding strategy usually requires significant simplifications in the fault description. In the subsequent gridding process, one is faced with two choices: The extrusion direction and the cell faces in the grid can be set to follow major fault surfaces, which gives grid cells that are not Korthogonal and hence susceptible to large discretization errors when used together with a traditional two-point method [see Aavatsmark (2007) and Wu and Parashkevov (2009)]. These discretization errors can be reduced by using a more-accurate discretization.…”

“…This will create cells that are mostly K-orthogonal and hence limit the two-point discretization errors. Likewise, areal distortions can be reduced by using 2.5D Voronoi grids (Wu and Parashkevov 2009;Branets et al 2009). Another alternative is to use unstructured grids to adapt to complex fault networks (Gringarten et al 2008).…”

Enriched multi-point flux approximation for general grids

“…Unfortunately, K-orthogonality is often lost in the grids that honor the geologic features such as the sloping faults and channels, and other important features such as nearly horizontal wells [18]. Recently, Wu and Parashkevov studied the effect of non-orthogonality error of deviated grids on the flow solutions from the two-point flux, control volume method [35]. They concluded that for most practical cases the errors in horizontal flow are relatively small and the errors in vertical flow can be rather significant.…”