Dispersion in consolidated sandstone with radial flow

This paper presents some experimental and theoretical results for dispersion processes occurring in consolidated Berea sandstone with radial flow geometry. A comprehensive review of the derivation and application of several analytical solutions is also presented. The Galerkin finite element method is applied to solve the advection-dispersion equation for unidimensional radial flow.Individual and combined effects of mechanical dispersion and molecular diffusion are examined using velocity-dependent dispersion models. Comparison of simulated results with experimental data is made. The effect of flow rates is examined. The results suggest that a linear dispersion model,D=u, whereD is the dispersion coefficient,u the velocity and a constant, is not a good approximation despite its wide acceptance in the literature. The most suitable mathematical formulation is given by an empirical form of , whereD _ois the molecular diffusion coefficient. For the range of Péclet number (Pe=vd/D _m,wherev is the characteristic velocity,d the characteristic length andD _mthe molecular diffusion coefficient in porous media) examined (Pe=0.5 to 285), a power constant ofm=1.2 is obtained which agrees with the value reported by some other workers for the same regime.