A Volume-conserving Representation of Cell Faces in Corner Point Grids

Corner point grids are currently the standard representation for reservoir simulation grids. Cell faces in
corner point grids are traditionally represented as bilinear surfaces where the edges between the corner
points all are straight lines. This representation has the disadvantage that at pillar-gridded faults with
varying dip the cell faces on either side will not precisely match, giving overlapping cells or gaps between
cells. We propose an alternative representation for the cell faces. The four vertical cell faces are still
represented as bilinear surfaces, but instead of having linear edges between the cell corners along the top
and bottom faces, we propose a representation where all horizontal intersections through the grid give
straight lines between the grid pillars, giving column faces whose shape is independent of the corner point
locations of the individual grid cells. This ensures that the grid columns match up and that there are no
gaps or overlapping volumes between grid cells. This representation gives a local parameterization for the
whole grid column, and the top and bottom grid cell surfaces are modelled as bilinear within this domain.
Using this representation we get a parameterization of the grid cell which we use to calculate the cell
volume.