Upscale to a Flow Grid

Too Fine to Flow

The geological grid carries more cells than a flow simulator can afford, so it is coarsened to a simulation grid. But permeability cannot simply be averaged: the right effective value is the one that passes the same flow.

Bounds and the Right Answer

Flow along the layers gives the arithmetic mean, the upper bound; flow across them gives the harmonic mean, the lower bound. The flow-based effective permeability, from an actual single-phase flow solve, sits between the two, near the geometric mean for a random field. Coarsen the grid and that value holds, where a simple average would drift.

Spend the Cells Wisely

Upscaling is where the fidelity of the static model meets the cost of the dynamic one. Coarsen only as far as the flow-controlling features survive, and use a flow-based estimate where connectivity matters, so the coarse model still flows like the fine one.