Russian Journal of Earth Sciences
Vol. 4, No. 5, October 2002
Compaction in Media with Inner Boundaries
A. V. Karakin
Abstract
A general formulation of compaction problems is described and the classification of
these problems in accordance with boundary conditions is presented. A basically new
class of compaction boundary problems in a finite region with moving inner boundaries
is specified. New models of compaction describe porous media in which qualitative
microstructural changes and associated sharp changes in material properties take
place. At these time moments, the permeability of the medium drops to zero (at
minimum porosity) or the skeleton loses its cohesion and breaks down. In the latter
case, the porous medium is transformed into concentrated dispersive mixtures of the
suspension, emulsion or sol type. Phenomena associated with jump-like changes in
material properties and resembling phase transformations in homogeneous media arise
at inner boundaries. Several physicochemical and mathematical aspects of these
problems are discussed. Examples of analytical solutions of some problems are presented.
In particular, the related wave processes are analyzed. The theory of compaction has
numerous applications in geophysics and technological problems of the chemical,
petrochemical, food-processing and biochemical industries. This class of compaction
models is advantageous to the study of such processes. As an example, the paper
presents a review of several geophysical applications including problems of mud
volcanism, sedimentation and motion of partially molten mantle rocks.