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 Â» 1.2. It is also identified that the critical exponent and fractal dimension of pores, D, satisfy t Â» 0.8 (1 + 1/D).
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