Analysis of oscillatory fluid flow through rock samples

Oscillatory hydraulic tests were conducted on samples of two varieties of Fontainebleau sandstone differing in porosity and a stacked sample of the two varieties. Simultaneous measurements of the upstream and downstream pressures and the upstream fluid flow permit the calculation of permeability and specific storage by two methods, the conventional upstream-downstream pressure analysis and the upstream pressure-flow analysis. The pressure analysis yields a relatively constant permeability for the high-porosity sample at different effective pressures and oscillation periods, but slightly period-dependent permeability for the low-porosity samples and the stacked sample. The period dependence diminishes with increasing period. Estimates of specific storage capacity derived from pressure analysis appear problematic. For samples with the higher porosity, values are highly uncertain due to peculiarities of the solution space used to convert attenuation and phase shift to permeability and storage capacity. For the sample with the lower porosity and the stacked sample, normalized storage capacity values fall significantly below the physical limit constituted by sample porosity. The flow analysis yields well-constrained values of permeability and specific storage capacity for the sample with the higher porosity. For the samples with the lower porosity and the stacked sample, both parameters show a strong dependence on oscillation period. We suppose that the two methods probe different portions of the pore space and thus yield different results for heterogeneous samples when periods fall below a critical period estimated from the scaling relation for hydraulic diffusivity. Flow analysis probes the portion of the sample facing the upstream reservoir with a thickness approximated by the penetration depth. In contrast, the pressure analysis probes the dominant flow path connecting the sample ends. In samples with connected but stagnant pores, the storage capacity has two distinct contributions from an effectively storing porosity and an effectively conducting porosity. The observed period dependence of storage capacity probably reflects the shift in balance between the two contributors.