Detecting Scales of Heterogeneity of Fluid Flow in Laboratory and Field Experiments

Two hydraulic parameters govern fluid transport in rocks, permeability (transmissivity) and storage capacity (storage factor). Since long it has been recognized that rock samples yield on average much smaller permeabilities in laboratory experiments than formations of the 10 to 10000 m scale in field tests. It has been argued that this difference arises from differences in the scale and/or heterogeneity of the conduit networks. Yet, standard analysis of both laboratory and field tests mostly relies on relations for rocks that are homogeneous and isotropic at least in a statistical sense and obeying Darcy's law. In this case, the temporal and spatial variations of fluid pressure are governed by a diffusion equation with hydraulic diffusivity determined by the ratio between the ability to transport (permeability and viscosity) and store (specific storage capacity) fluid. We suggest that performing hydraulic tests with periodic pressure perturbations offers important insight into the extent of heterogeneity. The basic result of periodic testing is a set of dimensionless numbers, phase shift and attenuation between two pressure signals at different locations and/or between pressure and flow at the same location. The relations among these numbers can be predicted based on simple analytical models and thus provides a chance to check for consistency between test results and underlying evaluation model, e.g., assumptions regarding homogeneity. Furthermore, frequency variations permit to control the apparent penetration depth of the pressure perturbation and thus the spatial region that dominates the response owing to the simple scaling relation between passed time, the spread of a pressure perturbation and diffusivity. From a fundamental research interest, periodic testing also contributes to the understanding of the response to natural signals on various time scales, such as barometric pressure, tides, and seasonal charging/discharging by precipitation and evaporation where source geometry ranges from volumetric to areal to linear. Examples are given from laboratory testing and field studies. Laboratory tests on artificially heterogeneous samples provide a test for the sensitivity of the approach. While we cannot exclude that the observed variation of hydraulic parameters with applied oscillation frequency partly owes to the erroneous application of a model our tests indicate that heterogeneity exists on all scales. Networks can be interpreted to be composed of two types of conduits, one that dominates the efficiency of transport and the other contributing to storage depending on the time scale of pressure gradient variations.