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

Abstract

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 2AE10 )19 and 1AE10 )13 m 2 , 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.

Analysis of oscillatory fluid flow through rock samples

“…Hydraulic properties of the investigated samples are hardly affected by effective pressure (Figs 4 and 5) in accord with our expectations from ultrasonic measurements and inspection of scanning electron microscope (SEM) images (Song & Renner 2006a). Permeability and specific storage capacity generally exhibit a modest decrease with increasing effective pressure.…”

“…The increase in permeability values gained from the flow analysis that commences when oscillation periods decrease below the critical period (τ < 1, i.e. the penetration depth falls below the sample length) likely reflects the previously observed length dependence of the hydraulic properties of F5% (Song & Renner 2006a) (Fig. 7).…”

“…4). Permeability values, k P , reach a plateau value of (4.9 ± 0.3) × 10 −19 m 2 for periods larger than 100 s consistent with the harmonic average of the two parts (Song & Renner, 2006a). At shorter periods, k P -values decrease with deceasing period down to 2.9 × 10 −19 m 2 at a period of 20 s. At periods larger than 1000 s, flow analysis yields k F -values approaching the values gained from pressure analysis.…”

“…The response of F8% appears independent of oscillation period over the range of investigated conditions. The two varieties, F5% and F8%, differ in their relation to the percolation threshold (Song & Renner 2006a), the porosity of F5% is very close to the cutoff porosity and the one of F8% further away. Proximity to the percolation threshold and homogeneity in the above sense go hand in hand: a sample at the percolation threshold cannot be subdivided into smaller units with similar properties.…”

“…Two varieties of Fontainebleau sandstone (∼100 per cent qtz) with porosities of ∼8 and ∼5 per cent and high ultrasonic P-wave velocities measured on saturated samples of ∼5200 and ∼5500 ms −1 , respectively, were chosen because of their modest pressure-sensitivity in hydraulic properties (Song & Renner 2006a). For brevity, the two varieties will be addressed as F8% and F5%.…”