A microindentation scanner is constructed that measures the spatial fluctuation in the elastic properties of natural rocks. This novel instrument performs automated indentation tests on the surface of a rock slab and outputs 2-D maps of the indentation modulus at submillimeter resolution. Maps obtained for clean, well-consolidated, sandstone are presented and demonstrate the capabilities of the instrument. We observe that the elastic structure of sandstones correlates well with their visual appearance. Further, we show that the probability distribution of the indentation modulus fluctuations across the slab surfaces can be modeled using a lognormal probability density function. To illustrate possible use of the data obtained with the microindentation scanner, we use roughly 10 cm × 10 cm scans with millimeter resolution over four sandstone planar slabs to numerically compute the overall drained elastic moduli for each sandstone sample. We show that such numerically computed moduli are well modeled using the multicomponent form of the Hashin-Shtrikman lower bound that employs the observed lognormal probability distribution for the mesoscopic-scale moduli (the geometric mean works almost the same). We also compute the seismic attenuation versus frequency associated with wave-induced fluid flow between the heterogeneities in the scanned sandstones and observe relatively small values for the inverse quality factor (Q-1<10-2) in the seismic frequency band 102 Hz

Using an asymptotic methodology, valid in the presence of smoothly varying heterogeneity and prescribed boundaries, we derive a trajectory-based solution for tracer transport. The analysis produces a Hamilton-Jacobi partial differential equation for the phase of the propagating tracer front. The trajectories follow from the characteristic equations that are equivalent to the Hamilton-Jacobi equation. The paths are determined by the fluid velocity field, the total porosity, and the dispersion tensor. Due to their dependence upon the local hydrodynamic dispersion, they differ from conventional streamlines. This difference is borne out in numerical calculations for both uniform and dipole flow fields. In an application to the computational X-ray imaging of a saline tracer test, we illustrate that the trajectories may serve as the basis for a form of tracer tomography. In particular, we use the onset time of a change in attenuation for each volume element of the X-ray image as a measure of the arrival time of the saline tracer. The arrival times are used to image the spatial variation of the effective hydraulic conductivity within the laboratory sample.

An analysis is presented to show how it is possible for unconsolidated granular packings to obey overall non-Hertzian pressure dependence due to the imperfect and random spatial arrangements of the grains in these packs. With imperfect arrangement, some gaps that remain between grains can be closed by strains applied to the grain packing. As these gaps are closed, former rattler grains become jammed and new stress-bearing contacts are created that increase the elastic stiffness of the packing. By allowing for such a mechanism, detailed analytical expressions are obtained for increases in bulk modulus of a random packing of grains with increasing stress and strain. Only isotropic stress and strain are considered in this analysis. The model is shown to give a favorable fit to laboratory data on variations in bulk modulus due to variations in applied pressure for bead packs.

During drainage, as a voxel of porous material is being actively invaded prior to percolation, the invading nonwetting fluid cannot be transmitted to the neighboring downstream voxel until a critical nonwetting saturation (Snc) is reached. This occurs when the invading fluid forms a percolating path across the voxel. We present novel laboratory observations of gravitationally stable, air/water drainage in thin bead packs, with 2D saturation fields monitored at high spatial and temporal resolution using transmitted light. We also present Invasion Percolation simulations. Both show that Snc has a strong dependence on capillary number (Ca), Bond number (Bo), and voxel size (Lz). We propose a percolation model that describes the functional form of Snc(Bo,Ca,Lz). We also produce a new theoretical model for the macroscopic capillary pressure function Pc(Sw,Bo,Ca,Lz), where Sw is the saturation of wetting fluid in the voxel.

While it has been recognized that a large amplitude incident wave upon a dry fracture can exhibit nonlinear seismic wave scattering due to its stress-dependent mechanical compliance, the impact of pore fluid in the fracture and a fluid-filled poroelastic background medium-features common for fractures in the Earth-are not well understood. As a first step toward an understanding of the nonlinear poroelastic response of elastic waves in fractured media, analytical approximate formulas are used for the amplitude and phase of a normally incident plane wave using a perturbation method, assuming a fluid-filled, highly compliant nonlinear interface embedded in a linear poroelastic solid. The stress-closure behavior of the fracture is modeled by nonlinear, poroelastic displacement-discontinuity boundary conditions (a linear-slip interface). The theory predicts that the static ("Direct current," or DC) and higher-order-harmonic waves produced by the nonlinear scattering can be greatly reduced by the presence of fluid in the fracture. This, however, depends upon a number of parameters, including fracture compliance, fluid properties (compressibility and viscosity), and the permeability of the background medium, as well as environmental parameters such as the initial fluid pressure and stress acting on the fracture. The static effect produces low-frequency fluid pressure pulses when a finite-duration wave is incident upon the fracture-behavior unique to fluid-filled fractures within a poroelastic medium.