Statistical characterization and stochastic modeling of pore networks in relation to fluid flow

Flow properties of reservoir rocks can be computed from an accurate depiction of the porosity network in three dimensions available from synchrotron X-ray microtomography. In order to relate computed transport properties to the input dataset, the complex pore networks must be described statistically. A porous media description was deemed adequate if a synthetic medium, possessing similar transport properties, could be generated from acquired statistical information. Synthetic media, based upon Berea sandstone extended variogram statistics, were generated with an actual slice from a 3-D microtomographic image as conditioning data. Control of local porosity variation was observed to be important in the stochastic simulation of porous media by the simulated annealing method, as inclusion of this higher order constraint data reproduced natural variations observed in pore-size distributions. Realizations with the traditional variogram as the only target in the objective function did not honor pore-size distribution information. Permeability estimates by the lattice Boltzmann method indicated that the proper level of interconnectivity was not achieved during geostatistical modeling with only two point spatial statistics. Connectedness information, readily available from primary drainage capillary pressure data, forced permeability estimates of synthetic media in the direction of the permeability computed for the parent microtomographic image of Berea sandstone. As a result of this study, it was concluded that global spatial correlation statistics, for example, the traditional variogram, must be supplemented with local variability and connectivity information to adequately characterize a three-dimensional property distribution for fluid transport. Extended porosity spatial correlation structure, extracted from standard imaging techniques, and a capillary pressure drainage curve are perhaps sufficient to characterize a system in terms of pore size, connectedness, and permeability. However, more rapid algorithms are needed to introduce porosimetry information as standard practice in stochastic modeling by the simulated annealing method.