Experimental Investigation into the Scale Dependence of Fluid Transport in Heterogeneous Rocks

We investigated the dependence of hydraulic properties on the spatial scale of intrinsic and artificial heterogeneity, applying harmonic pore pressure testing to two varieties of Fontainebleau sandstone at various periods and effective pressures. Blocks with porosities of about 5 and 8% were chosen exhibiting a permeability of about 2·10⁻¹⁹ and 1·10⁻¹³ m², respectively. The permeability of the less permeable variety strongly depends on sample size. Artificial heterogeneous rock samples were prepared by stacking pieces of the two sandstone varieties perpendicular and parallel to the main flow direction. The perturbation of the fluid flow owing to the interfaces between pieces of the same variety is controlled by the orientation of and subordinately by the effective stress on the interfaces. Constraints on conduit geometry derived from the effect of interfaces indicate that interconnectivity is more important than pore radius at the lower porosity. The effective permeability of alternating stacks of the two varieties differs tremendously for the two interface orientations; arithmetic and harmonic averages coincide with the effective properties parallel and perpendicular to the main flow, respectively. When the oscillation period is varied two regimes are observed, one with constant permeability at long periods and a second with decreasing permeability for decreasing period at short periods. Order of magnitude considerations of penetration depth suggest that this period dependence may be related to heterogeneity.