Grid Orientation Revisited: Near-well, Early-time Effects and Solution Coupling Methods

Abstract

The grid orientation effect is a phenomenon which leads to the computation of fundamentally different solutions on grids oriented diagonal and parallel to the principal flow direction. Grid orientation remains an important consideration for many practical simulation studies, and renewed interest in gas injection processes motivates the revisiting of this classical problem. In this article, we show that there are aspects of the grid orientation effect that can be traced back directly to the treatment of early-time, near-well flow and therefore have a major impact on adverse mobility ratio displacements such as miscible or immiscible gas injection. The details of this effect mean that any uncertainty quantification study should account for the interaction of the near-well heterogeneity and the grid orientation effect. We also show how two possible methods-a well-sponge method and a local embedding technique-are able to produce a solution largely independent of grid orientation for single phase two-component miscible flow. Both methods are versatile in that they can be implemented on general grid topologies. They are illustrated on Cartesian grids for both the standard quarter five spot problem with two different grid orientations, and a problem with a single injection well and two producing wells at different angles to the grid lines. Our results show that it is possible to reduce grid-orientation effects for challenging adverse mobility ratio miscible displacements with only local treatments around the injection wells.

An $h$-Adaptive Operator Splitting Method for Two-Phase Flow in 3D Heterogeneous Porous Media

“…The corresponding saturation field is shown in Figure 4.8 at t = 7.773, corresponding to roughly 0.19 pore volumes injected (PVI). This flow field is in good agreement with the results previously obtained by Kozdon, Gerritsen, and Christie [47] and Edwards [33]. …”

“…Many such simulations involve adverse mobility ratio displacement; that is, the displacing fluid flows more easily through the porous medium than does the displaced fluid. For such cases, it has been demonstrated that numerical methods can suffer from fronts that are excessively smeared or that suffer from grid-orientation effects depending on whether flow is parallel or diagonal to mesh lines (see, for example, [47]). The grid-orientation phenomenon was first observed for immiscible displacement by Todd, O'Dell, and Hirasaki [78] in 1972.…”

“…Kozdon, Gerritsen, and Christie [47] noted that for some numerical schemes, with favorable mobility ratios, numerical solutions converge with grid refinement on both aligned and diagonal grids, while for unfavorable mobility ratios, convergence to the same solutions is not achieved with grid refinement. In order to verify that our numerical combination with adaptive grids is able to be used to obtain grid-independent solutions, let us consider results in which the mobility ratio is 30, i.e., the viscosity ratio μ w /μ nw = 1/30.…”

In Situ Thermal Remediation of DNAPL Source Zones

“…Since the resulting groundwater flow in the heated section was diagonal to the finite difference grid, grid orientation effects associated with upstream weighting of the advection terms were determined to be causing the excessive spreading of the tracer plumes (Kozdon et al, 2008). Consequently, the velocities obtained by the electro-thermal model were exported into a modified version of MT3DMS (Xheng, Wang, & Zheng, 1999).…”

Robust Multi-D Transport Schemes with Reduced Grid Orientation Effects

“…In previous work, we have shown that extended injection well models reduce GOE by removing near-well perturbations that are critical in triggering unstable modes in the solution (Kozdon et al 2008). In this paper, we focus on the numerical scheme used for the transport equations.…”