Flow and solute transport in saturated porous media: 1. The continuum hypothesis

The continuum hypothesis provides one alternative to dealing with transport phenomena in porous media. If adapted correctly, the continuum approach may be easier than dealing with the system at the microscopic level. However, to adopt the continuum approach to phenomena occurring in porous media, certain conditions and length scale constraints need to be satisfied. Failing to satisfy these conditions may restrict the use of this approach, and other sophisticated methods need to be devised. This article provides an overview of the conditions and length scale constraints needed to be able to adopt the continuum hypothesis. Two types of length scale constraints may be identified. The first type arises when establishing the conditions and requirements for proper upscaling; they are thus essential and hence have to be completely satisfied. They have been collected in four constraints. The second type represents those derived during mathematical manipulations and order of magnitude analysis to neglect higher-order terms. It will be shown that most of the second type of length scale constraints are automatically satisfied once the essential constraints are satisfied.