The Grid Orientation Effect

A Circle That Comes Out Lobed

Inject water into a uniform reservoir and the flood should spread outward as a circle, because the rock looks the same in every direction. On a coarse grid the simulated front does not stay circular: it advances further along the grid rows and columns than along the diagonals, so the circle is pulled out toward the grid axes. This is the grid orientation effect. Coarsen the grid in the widget to strengthen the distortion and watch the front pull toward the grid directions.

The Grid, Not the Rock

The proof that this is an artifact and not real physics is what happens when you rotate the grid. The rock has not changed, so a real front would be unmoved, but the distortion swings around to follow the new grid orientation. The cause is numerical dispersion: the error in the discretized flow equations is not the same along the grid as across it, and on a coarse grid that anisotropy is strong enough to visibly bias the front. It is the discretization leaking into the answer.

Living With It

The effect bites hardest in adverse-mobility floods, where a less viscous fluid pushes a more viscous one, and it can shift the predicted breakthrough between an injector and a producer depending only on how the wells sit relative to the grid. The classic defenses are to refine the grid, since a finer grid disperses less; to align the grid with the dominant flow direction between wells where the geometry allows; and to use a nine-point flux scheme that couples diagonal neighbors and restores more of the directional symmetry. Recognizing the effect is the first defense: a lopsided front on a coarse grid is often the grid talking, not the reservoir.