Hydrodynamic dispersion and pore geometry in consolidated rock

Abstract

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.