Upscaling of porous media

Geological modeling methods are able to build models of enormous complexity with help from modern computers. When engineers wish to simulate fluid flow through rocks, perhaps in connection with designing an oil recovery plan or minimising the risk from burying some toxic substance, they need to simplify the geological models. The reason for this is that flow simulation needs to solve large systems of linear equations which requires additional computer storage. They also need to step the flow model through many time levels. Thus it is necessary to reduce the memory and cpu requirements.

A simple example of such a simplification is when a set of electrical resistors, arranged in series, is replaced by a single resistor with a value given by the arithmetic average of the original set. For resistors read permeability, and for arithmetic average read harmonic average.

When we move to 2 or 3 dimensions, and are concerned with more complicated physics, the problem of replacing a detailed model by a simpler model so that the large scale behaviour of the system is honoured becomes very difficult, and very interesting.

Upscaling is closely related to homogenization theory, a branch of mathematics that studies, amongst other things, equivalent media in a rigorous way where the ratio of the small length scale of the details to the scale of interest is asymptotically zero.

People working in this area within OCIAM are

• Dr Chris Farmer

For detailed information see

• C L Farmer. Upscaling: a review. International Journal for Numerical Methods in Fluids, 40, 63-78 (2002).