Pore-scale permeability prediction using critical path analysis
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Using the principles set forth in percolation theory and critical path analysis (CPA), this thesis presents a method for constraining parameterized values of critical pore size and a cumulative volumetric density function using the shape and scale of accessibility functions and a mercury intrusion capillary pressure (MICP) data set. Constraints can be made without an independent pore size distribution measurement. These parameters can be combined with the percolation threshold corrected for finite sample size and electrical formation factor to determine permeability and to approximate pore size distribution. The analysis uses predetermined permeability, porosity, and formation factor values in Berea Sandstone and Racine Dolomite core samples to initially quantify parametrization values. The analysis also compares two methods of deriving critical pore size using the Washburn equation and using parameterized values. The thesis also takes an initial look at applying the method to different methods for parameterizing the pore size volumetric probability density function; first using a pore solid fractal (PSF) model known to be appropriate in natural porous media and then using a truncated power law (TPL) distribution for comparison.