A new fluid permeability estimation in periodic grain consolidation models and nonoverlapping and overlapping mono-sized sphere models of porous media
Two new and efficient fluid permeability estimation methods are proposed and applied to periodic grain consolidation models of porous media and nonoverlapping and overlapping mono-sized sphere models of porous media. The two methods use the average properties of continuous Brownian motion paths that initiate outside a spherical sample and terminate upon contacting the porous sample. The first method uses Brownian paths to calculate an effective capacitance for the porous sample, then relates the capacitance, via angle-averaging theorems, to the translational hydrodynamic friction of the sample. Finally, a result of Felderhof is used to relate the translational hydrodynamic friction to the permeability of the sample. For sphere packings of nonoverlapping and overlapping mono-sized sphere models of porous media, random sequential addition is used. To compute the electrical capacitance using Brownian motion paths, the first-passage algorithm of Given, Hubbard, and Douglas is used. The second method uses penetration depth, which is the average distance between the radial positions where the Brownian motion paths are terminated and the radius of the sample. The permeability is given as the square of the penetration depth. In our calculations, capacitance and penetration depth are obtained simultaneously. For the sampling of porous media, a new sampling method, the "sharp-boundary" method is proposed and used. Without a proper sampling, we could not specify the exact sample porosity. However, with the sampling method the two estimation techniques become reliable and accurate methods to compute premeability. For the nonoverlapping and overlapping mono-sized sphere porous media, our estimate with sampling size R = 15.0 is very good, while for the periodic grain consolidation models of porous media the unit capacitance estimate with sampling size R = 15.0 is lower than the Larson-Higdon calculation. However, the penetration depth estimate with sampling size R = 50.0 is in a good agreement with the Larson-Higdon calculation. It is expected that the two new methods also work for other general homogeneous and isotropic porous media.