Grant A. Gist

Hydrodynamic dispersion and pore geometry in consolidated rock

Experimental measurements of the dispersion of tracer particles in flow through natural porous media are compared with a percolation model. The experiments show that tracer dispersion is a sensitive function of the width of the pore‐size distribution as measured by mercury capillary pressure. Measurements of capillary pressure (or electrical conductivity) are used to estimate the geometric correlation length of the dominant flow path in the rock. Percolation theory is used to derive a power‐law relationship between the correlation length and the ratio of the dispersivity to the average grain size. The experimental value of the power‐law exponent is in agreement with the theoretical prediction. Measurements on samples containing a residual saturation of wetting epoxy show no significant change in dispersion behavior. This result mediates against dispersion models requiring trapping in dead‐end pores. Tracer concentration profiles exhibit anomalous long‐time tails in two cases. In carbonate rocks, we associate long‐time tails with macroscopic permeability heterogeneities. In sandstones, long‐time tails occur in samples with a very narrow pore‐size distribution. These samples may have permeability heterogeneities as a result of defects in the packing density. In the limit of low flow velocity, the long‐time tail disappears, suggesting a convective mechanism associated with flow heterogeneities at a millimeter‐or‐larger scale.

Seismic attenuation from 3‐D heterogeneities: A possible resolution of the VSP attenuation paradox

Seismic attenuation is dominated by scattering from heterogeneities. Absorption attenuation mechanisms are expected to be small for the conditions of typical seismic field data. Previous models of scattering attenuation in seismic data used a 1-D model of layered stratigraphy. A new 3-D model of scattering attenuation is described that accounts for lateral heterogeneities, such as variations in bed thickness. The method can include fractal correlations that are known to provide a good representation of heterogeneities in well logs. The 3-D scattering model increases both wave attenuation and the total velocity dispersion compared to 1-D models. The typical velocity dispersion between seismic data and sonic logs can be accounted for by scattering from fractally correlated 3-D heterogeneities. The 3-D scattering model predicts that both velocity and attenuation are anisotropic.

Numerical Simulation of Sandstone Velocities ; Porosity And Clay Dependence

An elastic network model is used to Calculate compressional and shear wave velocities in a sandstone. Springs are used to represent compressional, shear, and rotational forces between neighboring grains on a regular cubic lattice. Mineral components and pores are distributed at random on the lattice. The network model is used to calculate the dependence of wave velocities on porosity and clay content. The principal result is that for a random distribution of quartz, clay and water components, the velocities calculated from the elastic network are a linear function of both porosity and total clay content, and the coefficients in this bilinear relationship are in guantitative agreement with published experimental correlations for sandstone velocities.