Computer simulation of flow through porous media, as used in oil
groundwater production and waste disposal risk assessment requires
geological models of the geometry and properties of the rocks in the
subsurface. The properties that are interpolated by these models include
the porosity and the permeability.
Much of the raw data for geological models comes from seismic surveys
where sound is reflected from layers at depths of up to five miles or so.
This leads to a collection of points, that mark the depth of a layer,
augmented from actual depth measurements in wells. It is necessary to
find a surface that interpolates these points and is discontinuous at any
faults. The best interpolation methods involve solving partial
The property interpolations require a grid of 3D cells to be built.
Dividing complicated shapes in 3D into small pieces with a regular
is made possible by, again, solving partial differential equations. The
basic principle is to mimic heat conduction in the volume of interest,
where we heat one part of the surface of the volume of interest, cool
another part, and prohibit heat flow through the remainder of the
The surfaces of constant temperature then divide the volume into two.
These surfaces, in combination with other surfaces constructed in a
similar way can be used to build the grid of cells. Another approach to
grid generation uses an analogy with fluid flow such that the streamlines
of the velocity field are used to construct the grid lines.
Modeling the geometry of natural structures is challenging. There are
unsolved problems, and the solutions to these have many practical
People working in this area within OCIAM
For detailed information see