Gelation Model for Porosity Dependent Fluid Permeability in Porous Materials
Abstract: A statistical
theory of gel
formation in a
polymer matrix was used
to explain the dependence
of liquid permeability in porous materials. A porous material was
modeled as a dispersion of bubbles in a solid matrix. Bubbles were treated as monomers
and formation of infinite connected bubbles was treated as the formation of
gels in polymer. The theoretical predictions were in agreement with the
observed data for basalt andesits. The model can easily predict the percolation
threshold of porosity
at which the
permeability increases suddenly,
which depends on
the effective number
of nearest bubbles around a
selected bubble. Around the percolation threshold, the permeability satisfies a
scaling relationship with a critical exponent of t ª 1.2. It is also identified
that the critical exponent and fractal dimension of pores, D, satisfy t ª 0.8 (1
+ 1/D).
Keywords: Gelation theory of
polymer, Porous medium, Fluid permeability, Percolation, Fractal dimension
Author: Mikrajuddin Abdullah
and Khairurrijal
Journal Code: jpfisikagg090002
