Study on Multi-scaling Laws of Rock Structures Affecting Hydraulic Properties

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Spatial estimation of geologic attributes requires extension of their properties, which are obtained from borehole cores and sampling at restricted points, to field scale. Therefore, scaling law, which relates data distributions at different scales, is indispensable to obtain detailed spatial model over wide area. Although fractal has been generally used as such a scaling law, it doe not consider spatial correlation structures specific to geologic attributes. We clarified that simulated annealing (SA) method, which adjusts the semivariogram of data selected randomly from the histogram to the semivariogram model defined, was the most suitable to spatial estimations at different scales, and proposed a new combination of scaling laws for the data and semivariogram.The SA was used for a pore distribution modeling in geologic media using bubble concrete material as a simulated porous rock. Pore distributions at several scales, 1×1 cm^2, 5×5 cm^2, 10×10 cm^2, 50×50 cm^2, 1×1 m^2, and 5×5 m^2, were modeled from the sectional pore data of cylindrical samples with 5 cm in diameter and 10 cm in height. The two scaling laws of pore radius on the semivariogram and histogram were used. Although the porosity was fixed, pores were connected largely with the increase of scale. This simulation result is also used to examine the effect of connectivity on hydraulic conductivity by comparing the hydraulic test results, which contributes to interpret the scale effect of hydraulic conductivity and estimate it at regional scale. The proposed method was also applied to the Berea sandstone samples, one of the well-studied porous sandstone over the world, and clarified a similar trend found in the simulation for the bubble concrete materials.