What PEBI means
PEBI stands for perpendicular bisector. Build a grid from a set of node points, connect each pair of neighboring nodes, and put the face between them on the perpendicular bisector of that connecting line. Do this everywhere and every cell becomes the region of space closest to its own node — a Voronoi cell. “PEBI grid” and “Voronoi grid” name the same object; reservoir engineers tend to say PEBI.
Why simulators want orthogonality
Most reservoir simulators discretize flow with a finite-volume two-point flux approximation (TPFA): the flow across a face is computed from the pressures in just the two cells that share it. TPFA is only consistent when the grid is K-orthogonal — the line joining two cell nodes must align with the permeability tensor acting on the shared face’s normal. For isotropic permeability that reduces to plain geometric orthogonality, and a PEBI grid delivers it by construction: the node-to-node line is, by definition, perpendicular to the shared face.
That is why PEBI grids have been a staple of reservoir simulation since the early 1990s — they hand the solver exactly the geometry its flux scheme assumes, which cuts grid-orientation error. When permeability is strongly anisotropic, TPFA can still err; engineers then build a permeability-aligned PEBI grid or move to a multipoint flux scheme, but the orthogonality argument otherwise holds.
Honoring faults and wells
Because you control where the nodes go, you control where the faces land:
- Faults: place nodes so cell faces fall on the fault plane, and the fault becomes a real face in the mesh instead of a stair-step. See fault-conforming grids.
- Wells: refine radially around a wellbore to capture near-well pressure gradients, blending smoothly into the coarser field with no hanging nodes.
- Features and boundaries: cell size can vary gradually, so refinement is local and gap-free.
How AutoMesh-Geo helps
AutoMesh-Geo generates conforming PEBI (Voronoi) grids directly from a faulted, layered structural model, keeping the orthogonality reservoir solvers need while honoring faults and wells as hard constraints. It is a core capability for oil & gas and subsurface work.