NETWORK MODELING OF PERMEABILITY EVOLUTION DURING CEMENTATION AND HOTISOSTATIC PRESSING

Permeability of rocks may evolve as a complicated function of porosity during hydrothermal compaction. Recent laboratory studies on hot-pres sed calcite and naturally lithified Fontainebleau sandstone reveal tha t there exist three regimes with distinctly different permeability-por osity relationships. At relatively high porosities, permeability chang es with porosity reduction following a power law (k(proportional to)ph i(alpha)) with an exponent alpha approximate to 3 (regime 1). At low p orosities, the power law no longer applies and an accelerated reductio n in permeability is found (regime 2). Finally, the permeability becom es too small to be measured, which implies that the pore space is disc onnected and there is no percolation (regime 3). Similar behavior and three separate regimes have also been observed in the evolution of ele ctrical conductivity with porosity in hot-pressed quartz. In this stud y, we developed a unified model based on percolation theory and the si mulation of random networks to analyze the evolution of permeability a nd electrical conductivity in regimes 1 and 2. We incorporated a rando m shrinkage model and a connectivity loss model in a three-dimensional cubic network to account for the two distinct regimes. In regime 1; w e kept the network connectivity at 100% and reduced the diameter of an arbitrary bond by a shrinkage factor randomly distributed between 0 a nd 1. In regime 2, we reduced the network connectivity from 100% to th e percolation threshold while maintaining the same pore size distribut ion. For Fontainebleau sandstone, the pore size distribution is constr ained by microstructural observations from automated image analysis an d stereological measurements. For hot-pressed calcite and quartz, sinc e microstructural data were not available, we made preliminary measure ments on one available micrograph of a calcite sample. Our simulations predict changes in permeability and pore statistics as a function of porosity which Show good agreement with the laboratory data. In accord ance with percolation theory, the ratio between interconnected and tot al porosities is given by the ratio between the order parameter and th e bond occupation probability of the network. Detailed observations of the interconnected porosity and total porosity of calcite during hot isostatic pressing are in good agreement with the theoretical predicti on. Implications of our modeling results on the kinetics of healing an d diagenetic processes are also discussed.